quiz6solns

# quiz6solns - STA 4321/5325 — Spring 2010 Quiz 6 — March...

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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 denote the probability density function of a gamma random variable with parameters 0/, and ﬁ. “30) _ Wag—16‘; , for x Z 0 0 , for ac < 0 Then the value of fooo mge’gdx is (a) 1 «=72, F11. (M 00 >4 3 r. ’8 H, jKLc'lelx—r F(v<)-)‘§>°<=F(*3)*1=l.*1 =_: (d) 48 ‘3 Problem 2 Let X be a normal random variable with parameters a = 2 and a2 = 5. Then (a) E(X2)=4 V(X)= E()(L) ‘_ (ELK) L. (b) E(X2)=5 ‘ L (c) E<X2)=7 1206‘) .7 \/,(x) T £309) =—>'§+a_'" ’ c—a Problem 3 The exponential random variable is a special case of the gamma random variable with a = 1. This statement is ,‘fmm fFa‘W-W‘ (4), Plus in dt/l la it“. WWL" (b) False , -X. 2L 1,...» . 4' p 4 — P ftx)’ muff X C '73,; ’ X20 ‘. / D,w. O Problem 4 Let Z be a standard normal random variable. Then P(—2 < Z < 2) is roughly (a) 50% 15a “'36- 773-10 ML; of 14:le elusﬂh, (b) 68% Wut<z)=Y(°~l-1<’c<°”‘) d 99.7% H ‘FQP'JLG’<QZCFTZO’) Problem 5 Let X has a beta distribution with a = 1 and B = 1. Then P(O.2 < X < 0.8) is (a) 0.2 (b) 0.5 (d) 0.8 Note that the density function of beta random variable is f(w)= %%w”‘1(1—w)3’1 vaFOSIESl 0 ,WWW u—wx (10”) 'xV'll’UH: CL 1 if, 05x44 fog): puma) 0 / o’w. 05’ 0,? —; o%’02:06 0.1, " ...
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## This note was uploaded on 08/05/2011 for the course STA 4321 taught by Professor Staff during the Fall '08 term at University of Florida.

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quiz6solns - STA 4321/5325 — Spring 2010 Quiz 6 — March...

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