Stat225 Quiz 5 SolutionsA+++++++
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STAT 225 Quiz 5
The PDF of the continuous RV Y is given below.
fY (y) =
c(y2 + 1) if 0 < y < 2
0 otherwise
1. Find the value of c that makes this a legitimate PDF. (5 points)
2. What is the probability that Y is greater than 1? (6 points)
3. Find E(Y ). (4 points)
E[X] =
R 1
1 xfX(x)dx
E[X2] =
R 1
1 x2fX(x)dx
Var(X) = E[X2] E[X]2 FX(x) =
x R
1
fX(t)dt
STAT 225 Quiz 5
October 23, 2013
NAME:
Directions: You have 10 minutes to complete the quiz. You are allowed a calculator as speci ed in the
syllabus. If necessary, round decimal answers to 4 signi cant digits. Show all work to receive full credit.
Instructors will not interpret questions for you.
The PDF of the continuous RV Y is given below.
fY (y) =
3
26y2 if 1 < y < 3
0 otherwise
1. Find the CDF of Y . (6 points)
2. What is the probability that Y is between 1.5 and 2.5? (4 points)
3. Find the median of Y . (5 points)
E[X] =
R 1
1 xfX(x)dx
E[X2] =
R 1
1 x2fX(x)dx
Var(X) = E[X2] E[X]2 FX(x) =
x R
1
fX(t)dt
STAT 225 Quiz 5
October 23, 2013
NAME:
Directions: You have 10 minutes to complete the quiz. You are allowed a calculator as speci ed in the
syllabus. If necessary, round decimal answers to 4 signi cant digits. Show all work to receive full credit.
Instructors will not interpret questions for you.
The CDF of Y is below.
FY (y) =
8<
:
0 if y 0
1
63(30y y3) if 0 < y 3
1 if y > 3
1. Find the PDF of Y . (4 points)
2. What is the probability that Y is greater than 1 given Y is between 0.5 and 1.5? (6 points)
3. Find E(Y 2). (5 points)
E[X] =
R 1
1 xfX(x)dx
E[X2] =
R 1
1 x2fX(x)dx
Var(X) = E[X2] E[X]2 FX(x) =
x R
1
fX(t)dt
STAT 225 Quiz 5
October 23, 2013
NAME:
Directions: You have 10 minutes to complete the quiz. You are allowed a calculator as speci ed in the
syllabus. If necessary, round decimal answers to 4 signi cant digits. Show all work to receive full credit.
Instructors will not interpret questions for you.
The PDF of the continuous RV Y is given below.
fY (y) =
3
22(5 y2) if 0 < y < 2
0 otherwise
1. Verify that this is a legitimate PDF. (4 points)
2. What is the probability that Y is between 0.5 and 1.5? (7 points)
3. Find E(Y ). (7 points)
E[X] =
R 1
1 xfX(x)dx
E[X2] =
R 1
1 x2fX(x)dx
Var(X) = E[X2] E[X]2 FX(x) =
x R
1
fX(t)dt
stat225 Quiz 5 SolutionsA+++++++
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