# hw3_sol - Stat 503 Homework #3 -sol Due in class 9/16...

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Stat 503 Homework #3-sol Due in class 9/16 (80pts) 1.( 9pts ) Consider the population of tossing a die. The random variable Y is defined as following: 1, when get a even number Y= 0, when get a odd number (a) (3 pts) What type of the random variable is Y? Discrete random variable (b) (4 pts) Calculate E(Y) 1 ( ) Pr( ) 1(0.5) 0(0.5) 0.5 n i i E Y Y Yi (c) (3 pts) Calculate Var(Y) 2 2 2 1 ( ) ( ( )) Pr( ) (1 0.5) 0.5 (0 0.5) 0.5 0.25 n ii i Var Y Y E Y Y 2. (16 pts) Suppose we toss two dies, let X1 and X2 be the numbers of each toss. (a) (4pts) What is the Pr(X1+X2<5) Outcome: 2-- (1,1) 3---(1,2) (2,1) 4---(1,3) (2,2) (3,1) P=1/36+2/36+3/36=6/36=0.167 (b) (4pts) What is the Pr(X1-X2<5) P=1-1/36=35/36 (c)(4pts) What is the E(2X1-X2) E(X1)= E(X2)=(1+2+3+4+5+6)/6=3.5 E(2X1-X2)=2E(X1)-E(X2)=E(X1)=3.5 (d) (4pts) What is the σ(2X1-X2) E(X1 2 )=(1+2 2 +3 2 +4 2 +5 2 +6 2 )/6=15. 17 Var(2X1-X2)=4Var(X1)+Var(X2)=4{E(X1 2 )-[E(X1)] 2 }+ E(X2 2 )-[E(X2)] 2 =5(15.17-3.5 2 )=14.6 σ(2X1-X2)=sqrt(14.6)=3.82

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3.( 15pts ) In the united States, 42% of the population has type A blood. Consider taking a sample of size 4. let Y denote the number of persons in the sample with type A blood. Find (a) (3 pts) Pr{Y=0}=0.58 4 =0.1132
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## This note was uploaded on 09/26/2010 for the course STAT 503 taught by Professor Staff during the Fall '08 term at Purdue University.

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hw3_sol - Stat 503 Homework #3 -sol Due in class 9/16...

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