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Unformatted text preview: STA 4321/5325 — Spring 2010 Quiz 7 — April 2 Name: KEY There are ﬁve problems in this quiz. Each problem has exactly one correct answer. Problem 1 The moment—generating function of a continuous random variable X with a
probability density function f (ac) is given by (a) ff; mf(m)da: (bx . l' 3, 1
(b) f0; $2f($) dcc PMJ S E & ) — Tatx. {Ln} .lK
(0) f0; ezf(ac) )dm . (d) ff; etmf(x)d:r Problem 2 Let M X( ) be the moment generating function of the random variable X. The kth derivative of M X( ) is given by M ( Xt)( t): $5M X(t) Then the second moment of X be can
calculated by (a) MEMO) m <4,qu (“p/W" o x :6 EKXL) ,
() V(X) . L I 33— Mlg bl.) = MLL) *zo
(d) (Em? £6) av X ( ) Problem 3 The moment—generating functions are unique; that is, two random variables that
have the same momentgenerating function have the same probability distributions as well. This
statement is (b) False Problem 4 Let X have a mixed distribution F(X) writen uniquely as
F(X) = cF1(X) —— (1 — c)F2(X) where F1 is the distribution function of a discrete random variable X1 and F2 is the distribution
function of a continuous random variable X2. Then E(X2) is (a) cE(X1) + (1 — c)E(X2)
(b) E(X1)+E(X2) (d) E(Xf) +E(X22) Problem 5 Let X has a gamma distribution with MX(t) = (1 7 ﬁt)_“. Then E(X) is (a) a (b) (w? 2w = mm] {QPW)’ (C) 0425 ll: >3 ...
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 Fall '08
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 Probability

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