The Poisson distribution for a discrete variable x = 0, 1, 2, ... and real parameter λ is (a) Prove that the mean of such a distribution is (b) Prove that the variance of such a distribution is (c) The mode of a distribution is the value of x that has the maximum probability. Prove that the mode of a Poisson distribution is the greatest integer that does not exceed λ, i.e., the mode is λ. (If λ is an integer, then both λ and λ − 1 are modes.) (d) Consider two equally probable categories having Poisson distributions but with differing parameters; assume for definiteness λ1 > λ2. What is the Bayes classification decision? (e) What is the Bayes errors rate?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 19E
icon
Related questions
icon
Concept explainers
Question
100%

The Poisson distribution for a discrete variable x = 0, 1, 2, ... and real parameter λ is

(a) Prove that the mean of such a distribution is

(b) Prove that the variance of such a distribution is

(c) The mode of a distribution is the value of x that has the maximum probability. Prove that the mode of a Poisson distribution is the greatest integer that does not exceed λ, i.e., the mode is λ. (If λ is an integer, then both λ and λ − 1 are modes.)

(d) Consider two equally probable categories having Poisson distributions but with differing parameters; assume for definiteness λ1 > λ2. What is the Bayes classification decision?

(e) What is the Bayes errors rate?

 

Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 4 images

Blurred answer
Knowledge Booster
Continuous Probability Distribution
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage