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stat200ch4_exercise1213soln

stat200ch4_exercise1213soln - Example Q X Y are independent...

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Unformatted text preview: Example Q X, Y are independent random variables ECX) = so , E(Y)=IOO I $900.18 , 599029, (a) EUOY) = IOE(Y) = IOLIOO) = 1000 V(|OY) = no2 vm = 100(9) = 3500 SDUOY) = \)3600 : 60 Lb) E(-5x+50) = —5E(x)+5‘0 = -5(So)+50 = -200 V(—5x+so) =(-5)2 wx) = 25(81): 1600 SD(-SX+50) = N300 = 40 (c) E(X+O.SY) = E(x)+ 0.5500 = 50+ 0,5000): [00 V(x+o.swr) : V(x)+ o.sf=vm bury?” S : 32+ 025(9): #3 a- ‘ b'o' SD (X+O.SY) :. J55 (d) E(x- Y) = 500 — EN) = 50—100 = -so v(x-Y) = v(x)+V(Y)= 82+61=too bgmflztfll SDLX‘Y) ‘7 ‘00 :10 0:1 [Dr-"1 (e) X,Y are correlated , p=05 E(x+¥)= E(X)+ Em: 130+— I00: IS'O V(X+ Y): VCx) +V(Y)+ 29 SDCX)SDLY) b'o Mays = 01-» L1+ 9m fitmrmz |4<g rm“ I: Exgmpl-e l3 Le+ X= amounf in fine small bowl y: amounf- in +he big bowl E(x)= LS , SD(X)=o.3 , EH): 2.5, 3000204 (O) TOTO! amoun+l'n 2 bowls = X+Y ECX+Y) = ECX')+E(Y) : I.S+ 2.5 = 4 ounces H$suming Hoe amounts in Has 2 bowls are independent, v(X+Y) : V(x) +v(Y-) :o.3’-+o.42=o,25' SD(X+Y) = J’o—QE = 0.5 ounces 1 (b) X+Y N N(}A=4, 0:05) P(X+Y7 4.5) : P((_x_ifl-_4 7 4‘S_ 4-) 0.5 0.5 i :- P(Z 7 I) ': : Jim-0.53) b3 68~QS—QQ.TI— " ///4: rule 4 4,5 sci-g = 0J6 ,. 4,27. / / ,, I ffim\ I“ (c) Le+ W: amoum of Cereal in He box E(W)= 16.3 ; SDCW)=O.‘2_ Rmoum- ER in the box .—. W- X—Y E(w—X—Y) = E(W)— 500— EU) : lb.3- I.5-— 2.5 =12.3 Ounces v(w—x-— Y) : V'(W) + V(x) + VLY) a$$umin9 w, x, Y are indep. : 0.2'z+.o.2>"+o.4z =o.'29 SD(W- X-V) : ’QR‘? OUHCQS xi = amoun+ m the CH1 SmaH bowl To+a\ Clmounf = XI + X1 m (w 9x 9) EH) 2 E(X1+X7_): E(X\)+E(Xz) = LS+L5 =3 ounces VF?) =1 VCXH'XTL) Z VKX15+ VCXZ) :: 0.32+O.31 : O.l8 SDU‘) = Jam = 0.429 ounce assuming X.,X7_ are Independent {finn‘ if. ...
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