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(c) Let N be the total number of trees in a forest, which follows a Poisson distribution with mean . The number of leaves on each tree follows a Poisson distribution with mean A, independently of all other trees. i. Let W be the total number of leaves in a forest. We can write W as а N W=X₁, with W= 0 when N=0. i=1 Write down the distribution of each X₁. F ii. Given N = n, state the distribution of W. iii. Find E(W) and Var(W). You can use the mean and variance of any standard distributions, as long as you state them clearly. loo...

(c) Let N be the total number of trees in a forest, which follows a Poisson distribution with mean . The number of leaves on each tree follows a Poisson distribution with mean A, independently of all other trees. i. Let W be the total number of leaves in a forest. We can write W as а N W=X₁, with W= 0 when N=0. i=1 Write down the distribution of each X₁. F ii. Given N = n, state the distribution of W. iii. Find E(W) and Var(W). You can use the mean and variance of any standard distributions, as long as you state them clearly. loo...

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.4: Expected Value
Problem 20E
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Automatic Zoom (c) Let N be the total number of trees in a forest, which follows a Poisson distribution with mean . The number of leaves on each tree follows a Poisson distribution with mean A, independently of all other trees. i. Let W be the total number of leaves in a forest. We can write W as N W = X₁, with W=0 when N = 0. A Write down the distribution of each X₁. i=1 ii. Given N = n, state the distribution of W. To... iii. Find E(W) and Var(W). You can use the mean and variance of any standard distributions, as long as you state them clearly. 12:39 7
Transcribed Image Text:Automatic Zoom (c) Let N be the total number of trees in a forest, which follows a Poisson distribution with mean . The number of leaves on each tree follows a Poisson distribution with mean A, independently of all other trees. i. Let W be the total number of leaves in a forest. We can write W as N W = X₁, with W=0 when N = 0. A Write down the distribution of each X₁. i=1 ii. Given N = n, state the distribution of W. To... iii. Find E(W) and Var(W). You can use the mean and variance of any standard distributions, as long as you state them clearly. 12:39 7
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