Math 3C Hour Exam Winter 2010.pdf

# I 24l 251 5 lb2y 11 sbi 2sbii5032 ibs7f problem ii 10

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'-\)~(. I) + ( 2.'4):l. (. \) "(2.5",)(.1) + (.%)(.5)"" {.lb){.2.y + (1.%)(.1) + (S.,b')(·I') = .2Sb+.I'i5+.032+ . \"Ib+.S7f, [=~~

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Problem Ii (10 pointe- 5 pointe each) Problem .. (10 poiDl&- 5 pointe each) A geiger oounter clicks, on a_, .""'Y 15 seconda. ABsumo that the number or clicks per mioute Follows a Poisson diotrihution. /I. = '-I CoDsider a game "here you contlDually roU a die until a 6 is rolled, endlDg the game. p = ~ ~eomeTr-i c. (a) Let X be the random variabl. "hich oounts the total number of clicks clicked game is ended? You may lea .. your _ in terms of P, C, I, sums, producls, (a) What is the prohability thai you'ha ... 10 flaY exactly 20 times until the by three Independent geipr oountero in a mlnute. How many cUcks per mJn::'::u::t=" _ is one standard deviation of X1 ,-- exponents, etc. .. :; lit +)t.z. +)1..3 ... _ J',r I )( = X en cwe ... "'~f>. '-\ clicl<S I .... i" p(p2ci)= -t'(1_t;)'2.0-1 V"'''' ()():.12 ), = E.)I. :. VCI'" ()(. '> = '-l \ cr "2-\3 (?\/\..L (. [:c~ ...;/ [l(%)\~J CT '" --1"1 "f2l '------' /' (h) What is the probehillty that you ha .. to play at leaet 20 times until the g ..... is ended? You me,y lea'" your _In terms of P, C,I, sumo, products, exponents, etc... (b) It is known that during one particular minute, one or the geiger oounters ,---) clicked at moot 3 times. What is the probability that tbe number or clicks L clicked by this oounter during the mioute ..... at lesst 2? You may lea"" your P(U2C'):' (1-i-)2.C>-1 answer in terms of. PI C, II BUDlB I product8 1 exponeD\a, etc. .. ? (X ~ 3) f(~~:.~ J:/ '?(2.~)( ~3.)= ?("'=2.') -To ? ()(. =3) \'" _~ -,\'"\3l ...1 i e V-\- e '?>~ / >:~ ]
( (. 2-1/ o.e)4 )< ~ D (e) (5 points) Let Problem 6 (25 polDts) ..f '- ("') - { -'"\o,e -"''' o if:z: <0 )I; ~o (a) (10 points) Let G(:z:) = :i' if 0 <:z: < 1 { 1 ifl\$:z: <:.0,.,.;;,., ... 0 .... \$ foe" ih<O be the distribution function c4 a continuous random variable Y.

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