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Exercise 2. Let p = [0, 1] and let random variables X₁,..., Xn be i.i.d., such that P(X₂ = 1) = p and P(X₂ = 0) = 1 - p for all i = {1,2,..., n}. Finally, let X be the average of the X₁. a) Determine E(X₂) and Var(X₂). b) Determine E(X) and Var(X). c) Show that P(X = k/n) = (^)p² (1 − p)ª-k.

Exercise 2. Let p = [0, 1] and let random variables X₁,..., Xn be i.i.d., such that P(X₂ = 1) = p and P(X₂ = 0) = 1 - p for all i = {1,2,..., n}. Finally, let X be the average of the X₁. a) Determine E(X₂) and Var(X₂). b) Determine E(X) and Var(X). c) Show that P(X = k/n) = (^)p² (1 − p)ª-k.

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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Exercise 2. Let p = [0, 1] and let random variables X₁,..., Xn be i.i.d., such that P(Xį and P(X₂ = 0) = 1 - p for all i € {1,2,...,n}. Finally, let X be the average of the X₁. a) Determine E(X;) and Var(Xį). b) Determine E(X) and Var(X). c) Show that P(X = k/n) = (n.) p² (1 − p)n-k. = 1) = p =
Transcribed Image Text:Exercise 2. Let p = [0, 1] and let random variables X₁,..., Xn be i.i.d., such that P(Xį and P(X₂ = 0) = 1 - p for all i € {1,2,...,n}. Finally, let X be the average of the X₁. a) Determine E(X;) and Var(Xį). b) Determine E(X) and Var(X). c) Show that P(X = k/n) = (n.) p² (1 − p)n-k. = 1) = p =
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