Unformatted text preview: ρ = cov( X 1 ,X 2 ) > 0. (a) Prove that there exists a standard normal random variable Z ∈ N (0 , 1) such that X 1 = ρX 2 + p 1ρ 2 Z. (b) Prove that Z is independent of X 2 . 2. • Exercise 4.2, page 127 • Exercise 5.3, page 129 • Problem #27, page 147 3. (a) If X ∈ U (0 , 1), show thatlog X has an exponential distribution. (What is the parameter of this exponential distribution?) (b) Determine the density function of n Y i =1 X i where X 1 ,...,X n are iid U (0 , 1) random variables....
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 Fall '08
 MichaelKozdron
 Normal Distribution, Probability, Variance, Probability distribution, Probability theory, probability density function, Cumulative distribution function

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