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quiz5solns

# quiz5solns - STA 4321/5325 — Spring 2010 Quiz 5 — March...

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Unformatted text preview: STA 4321/5325 — Spring 2010 Quiz 5 — March 19 Name: K E Y 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 non-negative values. Let f (us) denote the probability density function of X. Then (a) f(m) = 1 for every 1‘ < 0 (b) f(:v) = 0 for every cc < 0 (e) f(x) < 0 for every x < 0 ((1) f(x) = 0.5 for every :1: < 0 Problem 2 Let X be a continuous random variable with probability density function f (ac) and probability distribution function Then for each x E R, (a) F(x) = \$1790) (b) F (9:) = f2(£v) (C) F (03) = fix, f(y)dy (d) F (x) = ﬁg; Problem 3 Let X be a continuous random variable taking non-negative values, then E(X) = fO°°(1 — F(at))dx. This statement is (b) False Problem 4 Let X be the uniform random variable on the interval [530, 550]. Then (a) E(X) = 530 (c) E(X) = 550 (d) E(X) = 20 Problem 5 Let X be the exponential random variable with parameter 5. Then 4 @ HX2®=%u—€ﬂ Limb (b) P(X24)=1—e_ (c) 130(24): ée‘é UIIP (d) P(X 2 4) = e- Note that the density function of exponential random variable is Ag? ,forchO ,fora:<0 . %6 MO ...
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quiz5solns - STA 4321/5325 — Spring 2010 Quiz 5 — March...

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