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

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