Math 3C Final Winter 2010.pdf

# F r x 12 p c c x t ytqs y ol s laax1l z 3 tl oia sq i

• Test Prep
• DarkThunderKnight27
• 6

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f ()( >\ r;/ X / 1.2-) P C)<) C) X :::~~ t y\t\QS Y> ~Ol" S lAA'\X1,l , , -z- 3 :tL, '" OI.A S,Q.~ I : {J(X/l8 (\ X )lL) ~PC)(7\'6) . , 3( "'\.n-3 ) f(X)l~) r~')\~ rlx~~)::: ln~ f \-pJ = j?-:t2-_ ~f'/~ (1= ll()(j;)llf-)Vt) e (~)

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Problem 11 (40 point5- 10 points eech) You I.oss a weighted coin 150 times. The coin is weighted so that the probability AliSume thlll. X is nonnally distributed with mean ~ = -I IUld stlUldllrd devill- oC tOSiiing II head on II given toss is .6. p ~;·::;:;;~:;)·:o:>\ ~ t 0 45 == CJ,~~
Problem 13 (20 pointll- 10 poinls eBCh) (b) If U is unifOl"m1y difitributed on (1,,'i), fin.l E(b). (II) Suppose X ill a continuous random variable with distribution fundion o if%<O F(%) = 2:r-%~ if 0\$%<1 { 1 if 1:5 % Find the vllrillJloo or X. Leave your al1S1Irl'1 .., a fraction .1Jy..)=- r 0 X ~ 0 r~ ~ Ol - :2X 0 L. X ~ \ o X 2..\ ~(x):: 5~ X (2-2)<J =J ~ ~X -2x2-ax :=: X 1. _ -y-. 3 11 -::: \ -2" <%..L . .3 b 3 -3 ~(j2-).:: S~ X:>-(~-2tO= J~ 2-x Z-2x 3 clx CO L )( &_ ..1 X t.f I \:: 7- -1, =- .J, .3 ;} .... , 0 0 2.J ~ ) Prohlen. 14 (20 points- 10 point~ ellch) You roll two dice. Consider the following events: \ A = {llu:. hl'st dit! shuwn is Ii ::I} -- ~ B '" {The second die shown is a 3} C = {The sum of the two dice is odd} (a) Show that .4, Band C are pairwise indepel.ldent. (.) (A) ~J-0 ~l~)~ i fCc);; j.. Ov rJ ~ ( A0'0) -:: .L . .J-- ~ ..L ~J- / L 0b b0 V .., r(g(\c)?J~"k~ ~-~ V ~(t\(\c.)~1;-i~i-~ V

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• Summer '14
• N/A
• Math, Probability, Probability theory, probability density function, rplIol nllmbpr DPfinp, thst random child, probability mo.ss function

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