Fmd a deiiliity i t ile ifz 0 ncnecreosi3 function gz

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Fmd a deIIlIity I(~= t ile -:'" -if:Z: ~ 0 ncn~ecreos.i!"\3 function g(:z:) ~:or~Y:.:. _ What real number muot a be 1IO that I(:z:) is a probability dellllity function? --- ----"'t I ''\ £0 0 \ Ii'" .f ( ,,_ Ii "" '\. 2 if- 'l\ ~ I"ao JO <> ('0'> -41' c;.o"+''',,"o''"S', \( ",0· "; -.,..""" .. ~( .... J .1-00 of(")"",, ~ oJ o.e"d)< +-.In "e dll- = . glx/::, 3'1- ~ 0 "')<. <'1 \ / -'" 0 o,e c ::. o,e-"I/O) l 6;~ I> q \"'" ~e>< 1_00 +- -~e·)l c :.1 0.=<\ V 00 CI-:iZ +-...!L: \ '5 -u; c, I G::.~J (b) (10 polDts) IT X is the random variable wbose probability domsity function is I(:z:) from pan (a), find P(X $ 2). You may lea"" your answer in terms of a. F ()<.) ~ p (X :>)<.") ,-;:::=--_~ ~-- P()(~2)-\ { 1-F(2.) "\ ~\~ = 1- o.e" 01 .. -1:1. C\e-~)<,),'1 -00 0 , [email protected]><1 ::. \ - Clel< + --e.- 2 1-10:> "I t> = I' _ ~ ... .::l.. -2 0, ~ '"Ie -'1'"" r: 1 - 2-'L + -"- 0 I '"I "I e
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..... , Problem 7 (15 points) 2 2 2 Z 2. 2 ;:. 12 Six different pain of oocIcs (red, gray, blue, white, purple, greeD) are washed at a lauudromaL. However, ouly 9 oocIcs make it back home. What is the expected -~ Dumber of matehiog pairs of oocIcs that make it back home? Vou may lea"" your --j ( .......... in terms of P, C, !, 1IUDlIl,'Prodlicta, axpoDeDta, etc... o (~)(i)' , (I p<li r ):: (Ii) b p<lirS f I ,,",O<+ehi,,~ pC'li.- X" c "cr.- mOl+ cnin 9 ~ (~)( ~) E')(.,:: rlp, '" C;) '(= # tnC'lTc: hin 5 p",;rs +<7+-",,\ = X I ~ )(. l.. -+- X 3 -+ x., ~ X S- -+- Xli, EY;:. E(x'+')(.1.+ X3 +)c.'1+'X +)("&) 5 J~ ········6~ I (';) ';,(: ~ mc,+cni .... e p"'irs PoSSi\:>\e """lues ~ "?> or- '-I poI''-S 0"'1' WOl~.+ E.~. If;" R R \'3)"2-2-2 G G! EX:: P(x='3) + 1-1_ P(x=y) P()l,=3)= ('~) B B \N P 3 P(')(.='"1)=\- (%,)2 Gf'OI'j or (~) .f\ i-f.!"Ed. pOoir bel,,\< X reel = to C>'the.-"" ,'se ~ "..,<>rt-cI,'''B pOlif"S" X '+""2 + .. _.,.)(~ E'i.re<>l= OP('l<."-C;+P("""I).! b (,~) ( \ 0) ~ "':>+ f'ed Ey" ;:. P(ll.:\): ,._~"1~~_ SOc\<S ( \~) ('~) \ ,
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