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Unformatted text preview: STA 4321/5325  Spring 2010
Quiz 5  March 19
Name:
There are ﬁve problems in this quiz. Each problem has exactly one correct answer.
Problem 1 Let X be a continuous random variable which takes nonnegative values. Let f (x)
denote the probability density function of X . Then
(a) f (x) = 1 for every x < 0
(b) f (x) = 0 for every x < 0
(c) f (x) < 0 for every x < 0
(d) f (x) = 0.5 for every x < 0
Problem 2 Let X be a continuous random variable with probability density function f (x) and
probability distribution function F (x). Then for each x ∈ R,
(a) F (x) = d
dx f (x) (b) F (x) = f 2 (x)
(c) F (x) =
(d) F (x) = x
−∞ f (y )dy
1
f (x ) Problem 3 Let X be a continuous random variable taking nonnegative values, then
∞
E (X ) = 0 (1 − F (x))dx. This statement is
(a) True
(b) False 1 Problem 4 Let X be the uniform random variable on the interval [530, 550]. Then
(a) E (X ) = 530
(b) E (X ) = 540
(c) E (X ) = 550
(d) E (X ) = 20
Problem 5 Let X be the exponential random variable with parameter 5. Then
4 1
(a) P (X ≥ 4) = 5 (1 − e− 5 )
4 (b) P (X ≥ 4) = 1 − e− 5
4 (c) P (X ≥ 4) = 1 e− 5
5
4 (d) P (X ≥ 4) = e− 5
Note that the density function of exponential random variable is
f (x) = x
1 −β
βe 0 2 , for x ≥ 0
, for x < 0 ...
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 Spring '08
 Staff
 Normal Distribution, Probability, Probability distribution, Probability theory, probability density function, exponential random variable

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