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8/3/2019 com TARC STPM Trial 2011 Maths T Paper 2
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8/3/2019 com TARC STPM Trial 2011 Maths T Paper 2
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8/3/2019 com TARC STPM Trial 2011 Maths T Paper 2
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Th dascrete random 'anable X h th p r o b 4 b i h ~ functions _= .l ') = k ( t) for x =0, 1, 2 and - - - -P(Jf = = k(x - 2) for x = 3.(a) Show that k = t.(b) Find the mean and 'tariance of ..(c) Find Var(JX- 4) .
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The random variable Wis defined in [1. 4]. The prob3bitit) densit) function is ghen b}f{w) = A.(-wl + Sw - 4).(a ) Show that A.= i.(b) Detennine the cumulath e distnbution functt'- n. u ).
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Three friends, Mutu. Kai Li and .\li. go to u footh3l1 match but forget to say which entrance to the groundthey will meet at. There are four entnli\C' -4. B. l and D. Each friend chooses an entranceindependently. The probability that 't\{utu chooses entrance A is t .The probabilities that he chooses entrances B, Cor D are ali equal. Kai Li is equally likely to choose M ) of he tbur entrances
The probabilit) that Ali choo entrnnce C is .; and the probability that he chooses entrance D isf .The probabilities that he choos' the other t\ \ o entrances are equal.(i) Find the probability that at least 2 friend \\ ill choose entrance B.(ii) Find the probability that the three friends \\ ill all choo e the same entrance. (4][4)
The time spent surfing the i n t e n 1 e t ~ in hours. w "surve) d among a group of 60 students. The results ofthe survey is given in the table belo" .Time spent surfin.'{ 'hours) }lumber of tlldents0 x < 5- 55 lO 12
~ ~ < 15 1815 < \' < 20 820 _ y ,,-.. 1125 - -" ' .lS 6(a) Plot a histogram and estimnte the tnodnl surting time. [4)
[6]b) Calculate the median, mean and tn.ndard de\ inuon urfing time.The lifespan of a certain bmnd of plnsmu t e l ~ ' hnons ' normnlly distributed with a mean of .l years and astandard deviation ofo y e a r ~ It is kno'' th t sa.o of he tele' i aon have a lifespan of less than 3.2 yearsand 15% of the televi ion.; have a \ifesp m ofmore th m ) ars.(a)(b)(c)(d)
Calculate the value of ~ L a n d o . fSIDetermine the probahilit that :\ nmd :nnly sele-cted tel ' i wn lasts fe s than 3 years 9 months (2}If he warranty period of tlu bnmd (' f p l 1 l ~ m n tel ton t 3 years. find the expected percentage oftelevisions that fail within the wnrrnnt) p c r i ~ i fJJ10 televisions are randomly sclccttd. t'md the prohabthty b t exactly three of them will! st nt lca,t4 years. [31http://edu.joshuatly.com
