Let X₁, X2, X3, X4, X5 be an independent and identically random variables following a Binomial distribution with probability of success and 5 independent trials. a) What is the expected value of T = [(x₁² + X₁)? b) Find the probability distribution function of Y = 1 X₁. c) Find the mean and variance of Y = Σ₁1X₁. d) What is the P(0

A First Course in Probability (10th Edition)
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Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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2) Let X₁, X₂, X₁, X₁, X, be an independent and identically random variables following a
Binomial distribution with probability of success and 5 independent trials.
a) What is the expected value of T =
(X² + X₁)?
b) Find the probability distribution function of Y = 1X₁.
c)
Find the mean and variance of Y = ₁1X₁
d) What is the P(0 <Y ≤ 3)?
Transcribed Image Text:2) Let X₁, X₂, X₁, X₁, X, be an independent and identically random variables following a Binomial distribution with probability of success and 5 independent trials. a) What is the expected value of T = (X² + X₁)? b) Find the probability distribution function of Y = 1X₁. c) Find the mean and variance of Y = ₁1X₁ d) What is the P(0 <Y ≤ 3)?
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