Outline Thresholding: As thresholding increases intercomparisons of parameters become increasingly difficult Medium & High GDP/Capita – 80 Low GDP/Capita – 40 Regression Some Results The Big Ugly Table that you can’t read . Estimated in addition to actual populations, regression parameters etc. Some more results . A smaller table you might be able to read

Outline Thresholding: As thresholding increases intercomparisons of parameters become increasingly difficult Medium & High GDP/Capita – 80 Low GDP/Capita - 40 Regression Some Results The Big Ugly Table that you can’t read . Estimated in addition to actual populations, regression parameters etc. Some more results . A smaller table you might be able to read www.phwiki.com

Outline Thresholding: As thresholding increases intercomparisons of parameters become increasingly difficult Medium & High GDP/Capita – 80 Low GDP/Capita – 40 Regression Some Results The Big Ugly Table that you can’t read . Estimated in addition to actual populations, regression parameters etc. Some more results . A smaller table you might be able to read

Williams, Geoff, Contributing Writer has reference to this Academic Journal, PHwiki organized this Journal An Overview of Methods as long as Estimating Urban Populations Using Nighttime Satellite Imagery Paul Sutton psutton@du.edu Department of Geography University of Denver May, 2000 Outline ‘Known’ Population Data how good/bad is it Data: brief description of DMSP OLS imagery Estimating the Population of cities/urban clusters Estimating intra-urban population density ‘Temporally-Averaged’ Population Density Questions of spatial in addition to temporal scale Summary/Conclusions How Good are the numbers in addition to who cares When did the world population reach 6 billion Absolute population of Cities Mexico City U.S. Census Bureau 28 million United Nations 16 million Sao Paulo – U.S Census Bureau 25 million – United Nations 16 million Shanghai – U.S. Census Bureau 8 million – United Nations 15 million Istanbul – Nat. Geog. Atlas (1999) 2,938,000 [3,258,000] – Nat. Geog. Atlas (1995) 6,620,200 [7,309,200] Cited PRB in addition to U.S. Census Bureau Percent of Population Urban Models described here produce national population estimates very sensitive to these numbers. Errors inflate with increasing rural fraction of population Spatial Accuracy The 1994 Guatemala census included hundreds of populated places never previously enumerated. Nevertheless, the spatial characteristics of these data were rudimentary. The “maps” supplied to enumerators in some frontier districts were generally h in addition to drawn in addition to based on anecdotal in as long as mation. As a consequence, we have better in as long as mation than ever be as long as e regarding the size in addition to character of the Guatemalan population, we still lack a clear sense of where these people are.

Coker College SC www.phwiki.com

This Particular University is Related to this Particular Journal

Nighttime Satellite Imagery (DMSP OLS) ‘Percent Observation’ This hyper-temporal imagery used to measure urban areal extent Aggregate Estimation of Total City Populations Method I: Conterminous U.S. Imagery: DMSP OLS “Percent Observation” ‘Truth’: Wall to wall grid of Pop. Den. From 1990 Census Block Groups Method: Cluster adjacent pixels & Count them to measure Areal Extent of Cluster, overlay to obtain corresponding Population Method II: All Nations of the World Imagery: DMSP OLS “Percent Observation” ‘Truth’: Point Dataset of over 3000 cities with known population Method: Threshold, Cluster, & Count pixels as long as Area, Geo-reference & Overlay to obtain nationally specific slope & intercept parameters as long as the Ln(Area) vs. Ln(Popualtion) relationship from known cities, apply to all clusters Method 1: Proof of Concept with U.S. Data (Note: This also worked well with Mexico Data)

Method II: Going Global Use 1,383 Known Urban Populations to Estimate Populations of the 22,920 urban clusters found in DMSP OLS imagery Thresholding: Trade-off between too much conurbation in addition to ability to see small settlements Geo-Location: Provide each identified urban cluster with Country ID in addition to related national Stats Regression: Using Ln(Area) vs. Ln(Population) relationship to identify nationally specific slope in addition to intercept parameters as long as every nation Estimation: Estimate population of all 22,920 cluster with parameters in addition to use % urban statistic to get total national population estimate Thresholding: As thresholding increases intercomparisons of parameters become increasingly difficult Medium & High GDP/Capita – 80 Low GDP/Capita – 40 Regression Scatterplot of All Cities/Urban Clusters of the World w/ Known Populations All Cities (N= 1,404): Ln(pop) = .850 Ln(Area) + 9.107 R2 = 0.68 High Income Cities (N=471): Ln(pop) = 1.065Ln(Area) + 7.064 R2 = 0.77 Medium Income Cities (N=575): Ln(pop) = 1.011Ln(Area) + 8.174 R2 = 0.78 Low Income Cities (N=358): Ln(pop) = 0.989Ln(Area) + 8.889 R2 = 0.80 Venezuelan Cities (N=15): Ln(pop) = 1.164Ln(pop) + 6.475 R2 = 0.84

Example of estimating nationally specific regression parameters as long as Venezuela Some Results The Big Ugly Table that you can’t read . Estimated in addition to actual populations, regression parameters etc. Some more results . A smaller table you might be able to read

How did it go with the Biggest Cities Disaggregate or ‘Intra-Urban’ estimates of Population Density Allocate aggregate estimate of total city population to pixels within urban cluster Use linearly proportional relationship between light intensity in addition to population density Compare to residence in addition to employment based measures of population density Radiance Calibrated DMSP OLS images of Denver aka ‘Low-Gain’ or Light Intensity This imagery used to model intra-urban population density

Formal & Graphical Representation of the Model Actual, Modeled, in addition to Smoothed Representations of Minneapolis Some Results .

What do the Errors look like Temporally Averaged Population Density Census data is typically a residence based measure of population density People, work, shop, go to school, in addition to entertain & transport themselves outside of the home Is a temporally averaged measure of population density useful (e.g. as long as a given 1 km2 area with 600 people in it as long as 8 hrs, 300 in in the next 8 hours, in addition to 0 people in it the last 8 hours it has a temporally averaged population density of 300 persons/km2) Are DMSP OLS based estimates of population density a temporally averaged measure of population density

Questions of Spatial & Temporal Scale Is a population density dataset at a 1 km2 spatial resolution useful as long as Vulnerability studies L in addition to -use L in addition to -cover change studies Environmental Modeling What kind of temporal resolution of population density representations are useful in addition to needed What measures other than simple density are needed in addition to what means are there to acquire them When are errors of population numbers in addition to /or spatial location unacceptably large What’s Going on in 1 km2 Summary/Conclusions Nighttime Satellite imagery from DMSP OLS can be used to: 1) Estimate the population of urban agglomerations around the world 2) Estimate intra-urban temporally averaged measures of population density Continuing research will shed light on improved means of delineating areal extent of cities using the radiance calibrated datasets, better explanations of the national variations in the slope in addition to intercept parameters, in addition to a greater underst in addition to ing of the spatio-temporal nature of the population density estimates produced by these methods Future research should be in as long as med by the potential users of these datasets as to the spatial in addition to temporal scale required, in addition to the numerical in addition to spatial accuracy required There is potential as long as inclusion of these methods into the suite of tools used as long as conducting national censuses throughout the world

Williams, Geoff Entrepreneur.com Contributing Writer www.phwiki.com

Williams, Geoff Contributing Writer

Williams, Geoff is from United States and they belong to Entrepreneur.com and they are from  Irvine, United States got related to this Particular Journal. and Williams, Geoff deal with the subjects like Business; Entrepreneurs; Small Business

Journal Ratings by Coker College

This Particular Journal got reviewed and rated by Coker College and short form of this particular Institution is SC and gave this Journal an Excellent Rating.

 

Wind Tunnel Testing of a Generic Telescope Enclosure Experiment Scaling Experimental Setup Smoke Visualization

Wind Tunnel Testing of a Generic Telescope Enclosure Experiment		 Scaling Experimental Setup Smoke Visualization www.phwiki.com

Wind Tunnel Testing of a Generic Telescope Enclosure Experiment Scaling Experimental Setup Smoke Visualization

Dyer, Richard, Managing Editor has reference to this Academic Journal, PHwiki organized this Journal Wind Tunnel Testing of a Generic Telescope Enclosure Tait S. Pottebaum Douglas G. MacMynowski Cali as long as nia Institute of Technology June 2004 as long as merly D. MacMartin macmardg@cds.caltech.edu Experiment Model: Empty telescope enclosure Square opening size appropriate as long as roughly f/1.3 30° Zenith angle (fixed) Diameter = 0.83m, ~1% scale Turbulent flow at M2 location Probably not turbulent at M1 location Data: Flow visualization Digital particle image velocimetry (DPIV) data in a vertical plane containing the telescope axis near the dome opening Hot-wire anemometer data along the axis of the telescope Scaling Dimensionless parameters where L is the side length of the opening Convective frequency scaling Helmholtz frequency scaling where V is the enclosed volume in addition to c is the speed of sound

Coker College US www.phwiki.com

This Particular University is Related to this Particular Journal

Experimental Setup Clear Lucite dome with opening Camera in addition to mirror as long as visualization & DPIV Hotwire mounted on traverse Mirror in addition to optics as long as laser sheet Lucas adaptive wall wind tunnel 5’ by 6’ un-adapted Mounted on turn-table Large scale flow, 0° in addition to 180 ° Smoke Visualization 0° azimuth Smoke injected from outside the dome U

Velocity (hot-wire) spectrum inside enclosure 35m/s 20m/s data at 0°, r/R = 0.934 Large 2nd peak Dominant 1st peak fH fH -5/3 slope Shear layer modes: Frequency: f ~ 0.65nU/L Present as long as AZ 90° Mode n depends on speed; influenced by Helmholtz mode DPIV data Focus on area near the opening Principle of measurements Seed flow with tracer particles (water droplets) Illuminate a thin sheet with a laser (vertical plane on centerline of dome) Synchronize laser with the camera Record images in pairs with small time separation Correlate small regions of image to determine displacement Weaknesses In regions of steep gradients, velocity is typically underestimated Scales smaller than the interrogation regions cannot be resolved Only the in-plane components of velocity are measured Obtain mean in addition to statistics from large number of image pairs 2400 pairs as long as 0° 4495 pairs as long as 180° Sample data image: 1st snapshot

Sample data image: 2nd snapshot Mean in-plane velocity, 0° In-plane rms fluctuation, 0°

Mean in-plane velocity, 180° In-plane rms fluctuation, 180° Profiles on telescope axis

Conclusions Upwind viewing Shear layer across enclosure opening periodically rolls up into large vortices Frequencies are well described by convection velocity of shear layers in addition to a mode number Mode selection may be influenced by coupling of the shear layer instability with Helmholtz oscillations Large fluctuation velocities are likely to exert significant unsteady as long as ces on the secondary mirror in addition to support structure Downwind viewing Opening is inside the wake recirculation Mean velocity local maximum exists inside the dome Fluctuation levels are low, so most as long as ces are likely to be steady Further analysis Data being used as long as comparison with CFD (Konstantinos Vogiatzis, AURA NIO) Additional testing done with venting; data analysis in progress. Significant attenuation of shear layer modes

Dyer, Richard East Mesa Independent Managing Editor www.phwiki.com

Dyer, Richard Managing Editor

Dyer, Richard is from United States and they belong to East Mesa Independent and they are from  Apache Junction, United States got related to this Particular Journal. and Dyer, Richard deal with the subjects like Local News; Regional News

Journal Ratings by Coker College

This Particular Journal got reviewed and rated by Coker College and short form of this particular Institution is US and gave this Journal an Excellent Rating.

 

Lecture #9 Analysis tools in consideration of hybrid systems: Impact maps J

 www.phwiki.com

 

The Above Picture is Related Image of Another Journal

 

Lecture #9 Analysis tools in consideration of hybrid systems: Impact maps J

Coker College, SC has reference to this Academic Journal, Lecture #9 Analysis tools in consideration of hybrid systems: Impact maps Jo?o P. Hespanha University of California at Santa Barbara Hybrid Control in addition to Switched Systems Summary Analysis tools in consideration of hybrid systems?Impact maps Fixed-point theorem Stability of periodic solutions Example #7: Server system alongside congestion control server B rate of service (bandwidth) incoming rate q qmax q ? qmax ? r ? m r ? there is an asymptotically stable periodic solution

 Shostak, Seth Coker College www.phwiki.com

 

Related University That Contributed for this Journal are Acknowledged in the above Image

 

Example #7: Server system alongside congestion control q ? qmax ? r ? m r ? For given time t0, in addition to initial conditions q0, r0 If a transition occurred at time t0, when will the next one occur? right after one jump right after next jump impact, return, or Poincar‚ map Impact maps mode q* jump into mode q* (not necessarily from a different mode) Recurring mode ? q*2 Q such that in consideration of every initialization there are infinitely many transitions into q*, i.e., ? ? {q* = q, (q,x) ? F(q?,x?) } Definition: Impact, return, or Poincar‚ map (Poincar‚ from ODEs) Function F : Rn ! Rn such that if tk in addition to tk+1 are consecutive times in consideration of which there is a transition into q* then x(tk+1) = F(x(tk)) always eventually time-to-impact map ? function P : Rn ! (0,1) such that tk+1 ? tk = P(x(tk)) mode q2 mode q1 mode q3 mode q4 Example #7: Server system alongside congestion control q ? qmax ? r ? m r ? If a transition occurred at time t0, when will the next one occur? impact map time-to-impact map right after one jump right after next jump fixpoints.nb average rate?

Example #7: Server system alongside congestion control q ? qmax ? r ? m r ? x0 ? (1,1) x1 ? F(x0) x2 ? F(x1) fixpoints.nb the impact points eventually converge impact map time-to-impact map Example #7: Server system alongside congestion control q ? qmax ? r ? m r ? the impact points eventually converge congestion1.nb impact map time-to-impact map Contraction Mapping Theorem Contraction mapping ? function F : Rn ! Rn in consideration of which 9 g 2 [0,1) such that Lipschitz coefficient Contraction mapping Theorem: If F : Rn ! Rn is a contraction mapping then there is one in addition to only point x* 2 Rn such that F(x*) = x* in consideration of every x0 2 Rn, the sequence xk+1 = F( xk ), k ? 0 converges so that x* as k!1 fixed-point of F Why? Consider sequence: xk+1 = F( xk ), k ? 0. After some work (induction ?) This means that the sequence xk+1 = F( xk ), g ? 0 is Cauchy, i.e., 8 e > 0 9 N 8 m, k > N : ||xm ? xk|| ú e in addition to therefore xk converges as k ! 1. Let x* be the limit. Then F is continuous

Some Unique Trials 2008/2009/2010 Crop Group Validation – Brassicas Preliminary Data Global Residue Study – Tomatoes IR-4 Global Residue Project Public Health Project Public Health Project

Contraction Mapping Theorem Contraction mapping ? function F : Rn ! Rn in consideration of which 9 g 2 [0,1) such that Lipschitz coefficient Contraction mapping Theorem: If F : Rn ! Rn is a contraction mapping then there is one in addition to only point x* 2 Rn such that F(x*) = x* in consideration of every x0 2 Rn, the sequence xk+1 = F( xk ), k ? 0 converges so that x* as k!1 fixed-point of F Why? So far x* ? lim F(xk) exists in addition to F(x*) = x* (unique??) Suppose y* is another fixed point: x* must be equal so that y* Contraction Mapping Theorem Contraction mapping ? function F : Rn ! Rn in consideration of which 9 g 2 [0,1) such that Lipschitz coefficient Contraction mapping Theorem: If F : Rn ! Rn is a contraction mapping then there is one in addition to only point x* 2 Rn such that F(x*) = x* in consideration of every x0 2 Rn, the sequence xk+1 = F( xk ), k ? 0 converges so that x* as k!1 fixed-point of F Example: contraction as long as m < 1 Example #7: Server system alongside congestion control q ? qmax ? r ? m r ? the impact points eventually converge so that congestion1.nb impact map time-to-impact map Impact maps Recurring mode ? q*2 Q such that in consideration of every initialization there are infinitely many transitions into q*, i.e., ? ? {q* = q, (q,x) ? F(q?,x?) } Definition: Impact map Function F : Rn ! Rn such that if tk in addition to tk+1 are consecutive times in consideration of which there is a transition into q* then x(tk+1) = F(x(tk)) Theorem: Suppose the hybrid system has a recurring mode q*2 Q in addition to the corresponding impact map is a contraction the interval map is nonzero on a neighborhood of the fixed point x* of the impact map then it has a periodic solution (may be constant) the impact points converge so that the unique fixed point of F Impact maps Theorem: Suppose the hybrid system has a recurring mode q*2 Q in addition to the corresponding impact map is a contraction the interval map is nonzero on a neighborhood of the fixed point x* of the impact map then it has a (global) periodic solution alongside period T ? P(x*) (may be constant) the impact points converge so that the unique fixed point of F Why? Since F is a contraction it has a fixed point x*2Rn Take any t0. Since F(x*) = x*, q(t0) = q*, x(t0) = x* ) q(t0 +T) = q*, x(t0 +T) = F(x*) = x* Impact points are defined by the sequence x(tk+1) = F(x(tk)), which converges so that the fixed point x* Example #1: Bouncing ball x1 ú 0 & x2 < 0 ? x2 ? ? c x2 ? t time-to-impact map is not bounded below contraction mapping in consideration of c < 1 impact map time-to-impact map Impact maps Theorem: Suppose the hybrid system has a recurring mode in addition to the corresponding impact map is a contraction the interval map is nonzero on a neighborhood of the fixed point x* of the impact map then it has a periodic solution (may be constant) the impact points converge so that the unique fixed point of F Does not necessarily mean that the periodic solution is stable (Lyapunov or Poincar‚ sense) Is the periodic solution unique? yes/no? in what sense Impact maps the periodic solution is an ellipse any solution ?outside? is far from the periodic solution when x1 = 0 q = 1 q = 2 jump so that q = 1 (impact points) x1 x2 Impact maps Theorem: Suppose the hybrid system has a recurring mode in addition to the corresponding impact map is a contraction the interval map is nonzero on a neighborhood of the fixed point x* of the impact map then it has a periodic solution (may be constant) the impact points converge so that the unique fixed point of F Moreover, if the sequence of jumps between consecutive transitions so that q* is the same in consideration of every initial condition f is locally Lipschitz alongside respect so that x F2 (continuous-state reset) is continuous alongside respect so that x interval map is bounded in a neighborhood of x* then any solution converges so that a periodic solution every periodic solution is Poincar‚ asymptotically stable Impact maps Why? (since the sequence of jumps is the same we don?t need so that worry about Q) i) 1?3 guarantee continuity alongside respect so that initial conditions (on finite interval) ii) Therefore, if at an impact time tk, x is close so that the fixed point x* it will remain close so that the periodic solution until the next impact (time between impacts is bounded because of 4) iii) Moreover, if x(tk) converges so that x* the whole solution converges so that the periodic solution Stability from ii) convergence from iii) plus the fact that, from a Poincar‚ perspective, all periodic solutions are really the same (by uniqueness of fixed point) Moreover, if the sequence of jumps between consecutive transitions so that q* is the same in consideration of every initial condition f is locally Lipschitz alongside respect so that x F2 (continuous-state reset) is continuous alongside respect so that x interval map is bounded in a neighborhood of x* then any solution converges so that a periodic solution every periodic solution is Poincar‚ asymptotically stable Proving that a function is a contraction Contraction mapping ? function F : Rn ! Rn in consideration of which 9 g 2 [0,1) such that Mean Value Theorem: || F(x) ? F(x?) || ú g || x ? x? || 8 x, x? 2 Rn where A good tool so that prove that a mapping is contraction? A mapping may be contracting in consideration of one norm but not in consideration of another ? often most of the effort is spent in finding the ?right? norm contraction in consideration of || › ||1 not a contraction in consideration of || › ||2 (constant matrix in consideration of a linear or affine F) Stability of difference equations Given a discrete-time system equilibrium point ? xeq 2 Rn in consideration of which F(xeq) = xeq thus xk = xeq 8 k ? 0 is a solution so that the difference equation Definition (e?d definition): The equilibrium point xeq 2 Rn is (Lyapunov) stable if The equilibrium point xeq 2 Rn is (globally) asymptotically stable if it is Lyapunov stable in addition to in consideration of every initial state xk ! xeq as k!1. (when F is a contraction we automatically have that an equilibrium point exists & global asymptotic stability alongside exponential convergence) Impact maps Theorem: Suppose the hybrid system has a recurring mode in addition to the discrete-time impact system xk+1 = F(xk) has an asymptotically stable equilibrium point xeq the interval map is nonzero on a neighborhood of the equilibrium point xeq of the impact system then it has a periodic solution (may be constant) the impact points converge so that xeq Moreover, if the sequence of jumps between consecutive transitions so that q* is the same in consideration of every initial condition f is locally Lipschitz alongside respect so that x F2 (continuous-state reset) is continuous alongside respect so that x interval map is bounded in a neighborhood of xeq then any solution converges so that a periodic solution every periodic solution is Poincar‚ asymptotically stable Next lecture? Decoupling between continuous in addition to discrete dynamics Switched systems Supervisors Stability of switched systems Stability under arbitrary switching

Shostak, Seth Contributor

Shostak, Seth is from United States and they belong to Contributor and work for TechCrunch in the CA state United States got related to this Particular Article.

Journal Ratings by Coker College

This Particular Journal got reviewed and rated by and short form of this particular Institution is SC and gave this Journal an Excellent Rating.

 

Failure Time Analysis Outline Lecture Twelve

 www.phwiki.com

 

The Above Picture is Related Image of Another Journal

 

Failure Time Analysis Outline Lecture Twelve

Coker College, US has reference to this Academic Journal, Lecture Twelve Outline Failure Time Analysis Linear Probability Model Poisson Distribution Failure Time Analysis Example: Duration of Expansions Issue: does the probability of an expansion ending depend on how long it has lasted? Exponential distribution: assumes the answer since the hazard rate is constant Weibull distribution allows a test so that be performed

 Kostroff, Michael Coker College www.phwiki.com

 

Related University That Contributed for this Journal are Acknowledged in the above Image

 

Part II: Failure Time Analysis Exponential survival function hazard rate Weibull Exploratory Data Analysis, Lab Seven Duration of Post-War Economic Expansions in Months

Estimated Survivor Function in consideration of Ten Post-War Expansions

Painting a Self-Portrait: Resume Writing 101 Remember?? ONE IS THE MAGIC NUMBER! Your resume should fit succinctly on so that one page. Employer feedback indicates that resumes longer than one page are not preferable. Chronological Style Resumes: Suggested Headings Your Personal Heading Additional Heading Tips Education Heading (only post-secondary) Education-continued Experience Heading Experience Heading-continued Additional Tips Experience Additional Headings Helpful Hints: Career Planning Center Staff

Exponential Distribution Hazard rate: ratio of density function so that the survivor function: h(t) = f(t)/S(t) measure of probability of failure at time t given that you have survived that long in consideration of the exponential it is a constant: h(t) =

Interval hazard rate=#ending/#at risk Cumulative Hazard Function In general: For the exponential,

Weibull Distribution F(t) = 1 – exp[ S(t) = ln S(t) = – (t/a)b h(t) = f(t)/S(t) f(t) = dF(t)/dt = – exp[-(t/a)b](-b/a)(t/a)b-1 h(t) = (b/a)(t/a)b-1 if b = 1, h(t) = constant if b>1, h(t) is increasing function if b

Weibull Distribution Cumulative Hazard Function

Dependent Variable: LNCUMHAZ Method: Least Squares Sample: 2 11 Included observations: 10 Variable Coefficient Std. Error t-Statistic Prob. LNDUR 1.436662 0.103558 13.87303 0.0000 C -5.920740 0.403303 -14.68061 0.0000 R-squared 0.960092 Mean dependent var -0.409591 Adjusted R-squared 0.955103 S.D. dependent var 1.038386 S.E. of regression 0.220022 Akaike info criterion -0.013326 Sum squared resid 0.387276 Schwarz criterion 0.047191 Log likelihood 2.066628 F-statistic 192.4609 Durbin-Watson stat 1.210695 Prob(F-statistic) 0.000001 Is Beta More Than One? H0: beta=1 HA: beta>1, in addition to hazard rate is increasing alongside time, i.e. expansions are more likely so that end the longer they last t = ( 1.437 – 1)/0.104 = 4.20 Conclude Economic expansions are at increasing risk the longer they last the business cycle is not dead so much in consideration of the new economics maybe Karl Marx was right, capitalism is an inherently unstable system, subject so that cycles

Lab Seven

Cumulative Hazard Rate in consideration of Fan Failure y = 4E-05x + 0.0089 R 2 = 0.9816 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Duration in Hours Cumulative Hazard Lambda= 3.89 x 10-5, mean=25,707 hrs Regress Cumulative Hazard on Duration

Part IV. Poisson Approximation so that Binomial Conditions: f(x) = {exp[-m] mx }/x! Assumptions: the number of events occurring in non-overlapping intervals are independent the probability of a single event occurring in a small interval is approximately proportional so that the interval the probability of more than one event in an interval is negligible Example Ten % of tools produced in a manufacturing process are defective. What is the probability of finding exactly two defectives in a random sample of 10? Binomial: p(k=2) = 10!/(8!2!)(0.1)2(0.9)8 = 0.194 Poisson , where the mean of the Poisson, m, equals n*p = 0.1 p(k=2) = {exp[-1] 12 }/2! = 0.184

Kostroff, Michael Managing Editor

Kostroff, Michael is from United States and they belong to Managing Editor and work for Freedom Communications – Phoenix in the AZ state United States got related to this Particular Article.

Journal Ratings by Coker College

This Particular Journal got reviewed and rated by Lab Seven and short form of this particular Institution is US and gave this Journal an Excellent Rating.