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bution known as the Poisson distribution. Let r be a discrete random variable which can take the values 0, 1, 2, ... A quantity is said to be Poisson listributed if one obtains the value x with proba- bility -mm² P(x) = x! where m is a particular number (which we will show in part (b) of this exercise is the mean value of x). (a) Show that P(x) is a well-behaved probability distribution in the sense that Σ ΣP(x) = x=0 P(x) = 1. (Why is this condition important?) (b) Show that the mean value of the probability distribution is (x)=xP(x) = = m.

bution known as the Poisson distribution. Let r be a discrete random variable which can take the values 0, 1, 2, ... A quantity is said to be Poisson listributed if one obtains the value x with proba- bility -mm² P(x) = x! where m is a particular number (which we will show in part (b) of this exercise is the mean value of x). (a) Show that P(x) is a well-behaved probability distribution in the sense that Σ ΣP(x) = x=0 P(x) = 1. (Why is this condition important?) (b) Show that the mean value of the probability distribution is (x)=xP(x) = = m.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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This question is about a discrete probability distri- bution known as the Poisson distribution. Let æ be a discrete random variable which can take the values 0, 1, 2, ... A quantity is said to be Poisson distributed if one obtains the value x with proba- bility m I 'm² P(x) = x! where m is a particular number (which we will show in part (b) of this exercise is the mean value of x). (a) Show that P(x) is a well-behaved probability distribution in the sense that P(x) = 1. (Why is this condition important?) (b) Show that the mean value of the probability distribution is (x) = ΣxP(x) = m.
Transcribed Image Text:This question is about a discrete probability distri- bution known as the Poisson distribution. Let æ be a discrete random variable which can take the values 0, 1, 2, ... A quantity is said to be Poisson distributed if one obtains the value x with proba- bility m I 'm² P(x) = x! where m is a particular number (which we will show in part (b) of this exercise is the mean value of x). (a) Show that P(x) is a well-behaved probability distribution in the sense that P(x) = 1. (Why is this condition important?) (b) Show that the mean value of the probability distribution is (x) = ΣxP(x) = m.
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