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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...

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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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