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Assume that you have random variable X with the following probability density function with a > 0, b > 0: T(a+b) T(aT(6)"'(1 – x)°-1 if x € (0, 1) fx(x) = otherwise. (a) Suppose that a = 2 and b = 2. In this case, derive E[X] and var[X]. (b) Continuing with the X from part (a) with a = 2 and b = 2, let Z|X = x ~ Binomial(n, x). Find E[Z] and var[Z]. (c) Find the probability density function of Y defined by the following transfor- mation: Y = 1- X

Assume that you have random variable X with the following probability density function with a > 0, b > 0: T(a+b) T(aT(6)"'(1 – x)°-1 if x € (0, 1) fx(x) = otherwise. (a) Suppose that a = 2 and b = 2. In this case, derive E[X] and var[X]. (b) Continuing with the X from part (a) with a = 2 and b = 2, let Z|X = x ~ Binomial(n, x). Find E[Z] and var[Z]. (c) Find the probability density function of Y defined by the following transfor- mation: Y = 1- X

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Assume that you have random variable X with the following probability density function with a > 0, b > 0: Г(а+) I(a)T(b) (1 – x)b-1 if € (0, 1) -1 fx(x) = otherwise. (a) Suppose that a = 2 and b = 2. In this case, derive E[X] and var[X]. (b) Continuing with the X from part (a) with a = 2 and b = 2, let Z|X = x ~ Binomial(n, x). Find E[Z] and var[Z]. (c) Find the probability density function of Y defined by the following transfor- mation: Y = 1— Х
Transcribed Image Text:Assume that you have random variable X with the following probability density function with a > 0, b > 0: Г(а+) I(a)T(b) (1 – x)b-1 if € (0, 1) -1 fx(x) = otherwise. (a) Suppose that a = 2 and b = 2. In this case, derive E[X] and var[X]. (b) Continuing with the X from part (a) with a = 2 and b = 2, let Z|X = x ~ Binomial(n, x). Find E[Z] and var[Z]. (c) Find the probability density function of Y defined by the following transfor- mation: Y = 1— Х
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