# quiz6 - STA 4321/5325 Spring 2010 Quiz 6 March 26 Name...

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Unformatted text preview: STA 4321/5325 - Spring 2010 Quiz 6 - March 26 Name: There are ﬁve problems in this quiz. Each problem has exactly one correct answer. Problem 1 Let f (x) denote the probability density function of a gamma random variable with parameters α and β . f (x) = Then the value of ∞ 2 −x 2 dx 0 xe x 1 α−1 e− β Γ(α)β α x 0 , for x ≥ 0 , for x < 0 is (a) 1 (b) 8 (c) 16 (d) 48 Problem 2 Let X be a normal random variable with parameters µ = 2 and σ 2 = 5. Then (a) E (X 2 ) = 4 (b) E (X 2 ) = 5 (c) E (X 2 ) = 7 (d) E (X 2 ) = 9 Problem 3 The exponential random variable is a special case of the gamma random variable with α = 1. This statement is (a) True (b) False 1 Problem 4 Let Z be a standard normal random variable. Then P (−2 < Z < 2) is roughly (a) 50% (b) 68% (c) 95% (d) 99.7% Problem 5 Let X has a beta distribution with α = 1 and β = 1. Then P (0.2 < X < 0.8) is (a) 0.2 (b) 0.5 (c) 0.6 (d) 0.8 Note that the density function of beta random variable is f (x) = Γ(α+β ) α−1 (1 Γ(α)Γ(β ) x 0 − x)β −1 , for 0 ≤ x ≤ 1 , for x < 0 2 ...
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quiz6 - STA 4321/5325 Spring 2010 Quiz 6 March 26 Name...

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