Math 3c Review
Problems
1. Count all solutions to x + y + z = 100 if x > 2, y > 1, and z 0.
2. Let X, Y be uniformly distributed on [0, 1] and [0, 2] respectively.
Uniform Distributions
1.5
X (x)
Y (x)
Density
1.0
0.5
0.00.5
0.0
0.5
1.0
X, Y
1.5
2.0
2.5
(
Math 3C, Spring 2015
Practice nal
Last name
First name
Student ID
TA1
Section Time1
Question
1
2
3
4
5
6
7
8
9
10
Total
Points
10
10
10
10
10
10
10
10
10
10
100
Score
Good luck!
1
Write the TA and time of the section you are going to (but not necessarily
Miner
Math 3C (Tassy 12:00 PM): Solutions to Practice Final Exam
Problem 1
Let X be a continuous random variable with the following distribution function:
8
>0
x 0,
>
<
3.5
F (x) = x
0 < x 1,
>
>
:1
x > 1.
(a)
Find the density function of X.
The best way
Math 3C, Fall 2014
Midterm 1
Last name
First name
Student ID
TA1
Section Time1
Use the provided space for your solutions (you may use the additional page at the end). Show your work. Write only one solution
per problem - problems with multiple solutions w
Problem 1 (10 pts)
1. P (D) = P (Ac )
2. P (Dc |B) =
P (C) = 1/4
P (D c \B)
P (B)
= 1/2
Problem 2 (10 pts)
P (Rolling a vowel) = 2 1 +
6
2
3
20
1
2
=
29
120
Problem 3 (10 pts)
13
42
2
The rst term is the numbers of the two pairs and the second term is th
Problem 1
1) For fX to be a density function we need
+1
fX
+1
fX
=
1
+1
1
fX = 1. This impose:
2
+1
Cx
=
4
2
=
and C is 24.
2)If x < 2 the c.d.f is 0. If x
1
X
3
3 +1
]2
=
C
24
2 the c.d.f is given by:
=
x
=
F (x)
C[
x
fX (y)dy
2
24y
4
dy
2
=
1
X
3
24[
3
Math 3C, Spring 2015
Midterm 2
Last name
First name
Student ID
TA1
Section Time1
Question
1
2
3
4
5
Total
Points
10
10
10
10
10
50
Score
Use the provided space for your solutions (you may use the additional page at the end). Show your work. Write only one