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
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
=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4061eb31-6ba2-4539-9b51-dd7b05481e7e%2Faaf8c35d-a1c3-4d4b-ac4a-db0cb77c7758%2Fqfoc5y5d_processed.png&w=3840&q=75)
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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