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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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 Spring '08
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 Probability, Probability theory, 50%, α, 68%, 99.7%

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