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Stat 503 Homework #3sol
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(X1X2<5)
P=11/36=35/36
(c)(4pts) What is the E(2X1X2)
E(X1)= E(X2)=(1+2+3+4+5+6)/6=3.5
E(2X1X2)=2E(X1)E(X2)=E(X1)=3.5
(d)
(4pts) What is the σ(2X1X2)
E(X1
2
)=(1+2
2
+3
2
+4
2
+5
2
+6
2
)/6=15. 17
Var(2X1X2)=4Var(X1)+Var(X2)=4{E(X1
2
)[E(X1)]
2
}+ E(X2
2
)[E(X2)]
2
=5(15.173.5
2
)=14.6
σ(2X1X2)=sqrt(14.6)=3.82
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View Full Document 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.
 Fall '08
 Staff

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