stat400sln7 - U 0"‘5 “1.4 a u H [ DJ é“ D. H...

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Unformatted text preview: U 0"‘5 “1.4 a u H [ DJ é“ D. H 5.143 (a) P (0 g X g a H .o\u: use: 73 I a J % H l: (b) P(%SY31) I n H uh tote: h § § (0103 Q 11 & H 5% : A NH \__/ 03 B [I H cola! '5‘, H ’ mm: A ._. NIH S a: \ 1 N NH—I v =% (d) P(X Z 3:,Y Z 22—) x H “c 5,: l/\ x M r NIH IA >< IA 5 ll com I /"'\ 1 5.140 (a) f1(3:) : f0 (a:+y)dy — +ly21=$+1, 09:1, ‘ my 2 a 2 1 1 <1' mm = [(x+y)d:c=y+~, 0311-, 0 flaw) ll 1+3! ¢ (H (21+ :mxmm). a gm H 32 >4 Q3 1 '2 MN I Icn Y A q \__/ M ! ‘o-A H (2) Similarly, of, = ererjefefj 15 15 2Ti 256‘ (b) {X1 + X2 = 7} can occur in the two mutually exclusive ways: {X1 = 3,X2 = 4} and {X1 = 2, X2 = 5}. The sum of the probabilities of the two latter events is [%<;>7[%01+[;—;0>1 1.0 1.2 6.1—4 (3.) (/5 29—231 (13:1) 23‘222 (122) = ((5—1 — e‘2)(e‘1‘4 — 6—2") 0. 0.7 r = (0.368 — o.135)(0.247 ~ 0091) = (O.233)(0.156) ; 0.036. (b) Earl) = Em) = 0.5, E[X1(X2 — 0.5)2] = E(X1)Va1-(X2) = (0.5) (0.25) = 0.125. 6.1—8 P(1 < min Xi) = [P(1 < 2(1)]3 = (/we" )3 = e—3 = 0.05. 1 6.1—12 (a) P(X1 = 1)P(X2 =3)P(X3 : 1) z (2)2] = £94; (b) 3P(X1 = 3,X2 = 1, X3 = 1)+3P(X1 = 212 = 2,Xs = 1) = 27 27 162 3(1024) “(1024) ‘ 1024’ E[et(X1+X2)] : E[etX,]E[etX2] (<1 + 136‘)"1 (q + 126’)” = (q + pe’)"‘+"=- 6.2—6 My(t) = Thus Y is b(n1 + 122,?)- ". fl 6_2_8 E[et(x,+...+x,.)] : HE[etX;] = 118ch —l) “ ‘ i=1 i=1 : e(m+u2+---+1t.)(e‘-1), the moment generating function of a Poisson random variable with mean fl1+fl2+m+flm ...
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This note was uploaded on 07/24/2008 for the course STAT 400 taught by Professor Tba during the Fall '05 term at University of Illinois at Urbana–Champaign.

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stat400sln7 - U 0"‘5 “1.4 a u H [ DJ é“ D. H...

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