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solutionsexam1b - 1 The unfair die An unfair 6—sided die...

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Unformatted text preview: 1 The unfair die An unfair 6—sided die is two times as likely to roll a six as to roll a one. All other outcomes are equally likely. Compute the expected outcome, and the standard deviation. Now compute the expected sum, and standard deviation for three such die. Now compute the expected value and standard deviation for 3 times the outcome on one such die. r676) 1W3 :- 3.:)-ve¢f ; 91cm: WW) -: WOC) W303) two‘s) 2 The below table gives the percentage of the US. population in four regions of the United States as well as the percentage of social security recipients within each region. For the population of all social security recipients, what percent live in each of the four regions? Region Pct U.S. population Pct SS Recipients Northeast 15 Midwest 10 South Hint: This is just a Bayes’ Rule type question. Draw a tree and treat the percentages as probabilities A 3‘“ 3 Discrete Joint " Distributions Let X, Y each be either 1, ~1. Suppose that E(X) 2 EU!) = 0, show that: . lP(X=1,Y=l)=]P(X=—1,Y==—1) - 1P(X=1,Y= —l)=P(X=¥1,Y=1) Let p = 21P(X = —1,Y = -l). Find Var(Y),Var(X), CO’U(X, Y). W :) gm) 2 imam -:.-_~ éK -' Z IPCXm‘SYT?) X 7f | oDKKe/R’ *1) tf‘R/kcll yogi] ' This page intentionally left blank =2> (PG/=0 =51 :IW¥=~') 73 25,21: WWPGCW *qu’j/ Q _.. :2 l r; fC’U'é wajlgae\flj 40 ' ‘ ( :axv) rm‘w - 6%IXY) O H‘ " ,2 ( .g , (“PVC WM *— * WWW! (NJ? VH) {5-5 2£+£1 1.91%? .3 .‘2 Q 5‘ 10 4 Let X1,X2 N Eme), with X1 J. X2 What is the probability X1 5 X2? Let Z = X1 —u X2 What is E(Z)? What is Va'r(Z)? What is lP’(X1 < c,X2 > k)? 5 Short Answers 0 Find the probability distributions of boys and girls in families with three children. First assume that boys and girls are equally likely. Then assume that girls are twice as likely as boys. 0 Twelve people are to be selected to serve on a jury from a group consisting of 10 happy peeple and 15 angry people. If the selection is done randomly, what is the probability that all 12 are angry? o The number of possible outcomes of a ternary — (0, 1, 2) — k stage experiment is...? . Let z N N(0,1). What is 113(‘1 g z s 1)? What is lP’(—2 5 Z 5 2)?. What is M0 <_: Z 3 3)?. 13 ...
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This note was uploaded on 11/08/2009 for the course ISYE 2028 taught by Professor Shim during the Spring '07 term at Georgia Tech.

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solutionsexam1b - 1 The unfair die An unfair 6—sided die...

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