Math 3C Midterm 2.pdf

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3. Random variables: (d) (8 points) Suppose that the following table gives the probability density function for discrete random variable x: Create a table (a) (4 points) Define a random variable (the general definition, not for the cumulative distribution function for X and graph it. F( -::() the definition for continuous.or discrete random variables). ?t A r~f'ldo"" "~f'iCl\6Ie it c, - .f'~~C+"ol) f-r'o1Y\ ~ SClO\(J\.-e {pa"e. -n. ill+o II -!e"4- 61- -2- -/ ~. f' e-II \ I"\v.., b-t r' . -o.s- (b) (4 points) Define the expectation of a discrete random variable X. 'Ibis should involve a formula. I Fo." '1 dl~c.re+e ('4ndOfll \fQnQb~ 'X I --t+e.mf:-t4n ~ Ot"~"pet+ecJ Vc.lu -e of! ~ is. E(Y)::: ~ ~ RCIC;:")(1 / i v t--o ct./1O 0.\ ~(:x::~x.) F()():: _ \ 0 x,,-2. f{ , 'W"er~ -tkl, S\lIW\;1 ?( ovQ(' DIll v~IUt~ .A +f..e. rtH1~t 01 '12_ -2~')(~-1 '">< 'X Wi+" P(":X=~~ "'>0. (c) (4 points) Define the variance of a discrete random variable X. -I~"'t <: - n,is should involve a formula. "1,0 For Ct dikre+e.rCllldo~ va f'iob'e -.x Wlfh g/lo -a,s.!"",:, ('/ 'X-q)(iS is -x '(-a-",;s is F(~ t'rleq() ..A.<j;i.e v~"iQt)c-e ~ Y ,'s 'IGor' (x\:: '£, ("'(_~2. p(r~?() CY,o I~ ~ < 2- ..,.,. ~e~ -tte. oS U,,", il over CIIH "Ql\.1~S Ii') 11-e, ")(~"2 n-",-c.. O'f ~ wi...-h P(X~)o(}>O. 5 6 Pb;)~ P(-X"'~~) ~ Y.o ?i/o Mo 1,0 I
) ) 4. On Sunday, I went to Nasa's Jet Propulsion Lab for their annual open house. While there, let's say I coUected data on the heights and ages of random passers-by. The data is recorded on the last sheet (feel free to detach the sheet, there is no aeed to tum it in). Consider the age of the people to be one random va.riabl~,·taIl it A, and the height to be another, call it H.

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