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.
2. What is the probability that Y is greater than 1?
3. Find E(Y ).
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

Directions: You have 10 minutes to complete the quiz. You are allowed a calculator as specied in the syllabus. If necessary, round decimal answers to 4 signicant 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 . 
2. What is the probability that Y is between 1.5 and 2.5? 
3. Find the median of Y . 
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

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 .
2. What is the probability that Y is greater than 1 given Y is between 0.5 and 1.5?
3. Find E(Y 2).
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

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.
2. What is the probability that Y is between 0.5 and 1.5?
3. Find E(Y ).
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