Project 2
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PROJECT 2 - DUE FEBRUARY 12th, at 10am, after class ends
Chapter3: 1. For any probability function p(y),
∑ p( y) =1 if the sum is taken over all possible y
values y that the random variable in question can assume. Shat that this is true for:: a. the binomial distribution b. the geometric distribution c. the Poisson distribution
Chapter 4: 2. Let x be a random variable with probability density function Γ(α + β ) α −1 f ( x) = x (1 − x) β −1 , 0<x<1. Γ(α )Γ( β ) Γ(α )Γ( β ) . Γ(α + β ) 0 Find E(Xk) for the random variable X, with the pdf defined above. Then find the mean and the variance for the random variable X. 1
For α and β positive we also have that
∫x
α −1
(1 − x) β −1 dx =
Chapter 5: - Independent Study Section 5.7 3. Let X1 and X2 have the joint density function given by: 3 x , 0 ≤ x 2 ≤ x1 ≤ 1 f ( x1 , x 2 ) = 1 elsewhere 0, a. Find E(X2|X1=x1) b. Use Theorem 5.3 in your textbook to find E(X2)
Chapter3: 1. For any probability function p(y),
∑ p( y) =1 if the sum is taken over all possible y
values y that the random variable in question can assume. Shat that this is true for:: a. the binomial distribution b. the geometric distribution c. the Poisson distribution
Chapter 4: 2. Let x be a random variable with probability density function Γ(α + β ) α −1 f ( x) = x (1 − x) β −1 , 0<x<1. Γ(α )Γ( β ) Γ(α )Γ( β ) . Γ(α + β ) 0 Find E(Xk) for the random variable X, with the pdf defined above. Then find the mean and the variance for the random variable X. 1
For α and β positive we also have that
∫x
α −1
(1 − x) β −1 dx =
Chapter 5: - Independent Study Section 5.7 3. Let X1 and X2 have the joint density function given by: 3 x , 0 ≤ x 2 ≤ x1 ≤ 1 f ( x1 , x 2 ) = 1 elsewhere 0, a. Find E(X2|X1=x1) b. Use Theorem 5.3 in your textbook to find E(X2)
