Problems
373
PROBLEMS
7.1. A player throws a fair die and simultaneously
flips a fair coin. If the coin lands heads, then she
wins twice, and if tails, then one-half of the value
that appears on the die. Determine her expected
winnings.
7.2. The game of C

102
Chapter 3
Conditional Probability and Independence
PROBLEMS
3.1. Two fair dice are rolled. What is the conditional
probability that at least one lands on 6 given that
the dice land on different numbers?
3.2. If two fair dice are rolled, what is the co

50
Chapter 2
Axioms of Probability
which can be generalized to give
n
n
#
&
&
&
P(Ai )
P(Ai Aj ) +
P(Ai Aj Ak )
P Ai =
i=1
i<j
i=1
+ + (1)
n+1
i<j<k
P(A1 An )
If S is finite and each one point set is assumed to have equal probability, then
P(A) =
|A|
|S|

Problems
287
PROBLEMS
6.1. Two fair dice are rolled. Find the joint probability
mass function of X and Y when
(a) X is the largest value obtained on any die and
Y is the sum of the values;
(b) X is the value on the first die and Y is the
larger of the two

224
Chapter 5
Continuous Random Variables
A random variable is said to have a beta distribution with parameters (a, b) if its
probability density function is equal to
f (x) =
1
xa1 (1 x)b1
B(a, b)
0 x 1
and is equal to 0 otherwise. The constant B(a, b) is

Stat 200A Homework 2
(Due Wed. Oct 5 in class)
Note, the Problems and Theoretical Exercises are listed in separate sections at the end of the chapter.
1. Chapter 2, Problem 52
Solution. (a) There are 10
for each pair we can choose either
8 ways to select

16
Chapter 1
Combinatorial Analysis
PROBLEMS
1. (a) How many different 7-place license plates are
possible if the first 2 places are for letters and
the other 5 for numbers?
(b) Repeat part (a) under the assumption that no
letter or number can be repeated

Statistics 206
Homework 1
Due : October 3, 2016, In Class
1. Please tell true or false of the following statements with regard to simple linear regression.
(a) The least squares line always passes the center of the data (X, Y ).
(b) The true regression li

STA 200A: Homework 7
Due Wed. Nov. 9
Note: Below the notation 3.T11 means Chapter 3, Theoretical Exercise 11. Similarly, the notation 4.P21
means Chapter 4, Problem 21.
1. 6.P15
Solution:
(a) Let |R| be the area of R.
Z
f (x, y)dxdy = c|R| = 1
R
(b) Let 1

STA 200A: Homework 6
Due: Wed. Nov. 2 in class
Note: Below the notation 3.T11 means Chapter 3, Theoretical Exercise 11. Similarly, the notation 4.P21
means Chapter 4, Problem 21.
1. 5.T29
Solution: Let us assume that X has positive pdf over a region (a, b

STA 200A: Homework 6
Due: Wed. Nov. 2 in class
Note: Below the notation 3.T11 means Chapter 3, Theoretical Exercise 11. Similarly, the notation 4.P21
means Chapter 4, Problem 21.
1. 5.T29
2. 6.P10
3. 6.P14
1

Stat 200A Homework 1
(Due Wed. Sept 28 in class)
1. Ch. 1, Problem 1
Solution. There are 26 letters and 10 numbers (0-9), which means there are 262 (105 ) = 67, 600, 000.
We need to select 2 numbers in order, of which there are 26(25) outcomes, and 5 lett

STA 200A: Homework 5
Due Wednesday October 26
1. Let X Gamma(, ). Find E[1/X].
2. Let X Uniform[0, 1], and put Y = X. Find E[Y ].
3. Let X be an Exponential() rv. Derive a formula for E[X 2 ].
4. Find the density function of Y = eZ , where Z N (, 2 ). Thi

STA 200A: Homework 4
Due Wednesday October 19
Note: Below the notation 3.T11 means Chapter 3, Theoretical Exercise 11. Similarly, the notation 4.P21
means Chapter 4, Problem 21.
h
i
1
.
1. Let X be a Poisson rv with parameter . Calculate E X+1
2. 4.T10
3.

STA 200A: Homework 3
Due Wednesday October 12
Note: Below the notation 3.T11 means Chapter 3, Theoretical Exercise 11. Similarly, the notation 4.P21
means Chapter 4, Problem 21.
1. Three cooks A,B,C, bake a special cake and with probabilities 0.02, 0.03,

STA 200A: Homework 8
Due Wed. Nov. 16
Note: Below the notation 3.T11 means Chapter 3, Theoretical Exercise 11. Similarly, the notation 4.P21
means Chapter 4, Problem 21.
1. 6.P54
2. 6.P55
3. 6.T35
4. 7.P4
5. 7.P12
6. 7.P19
7. 7.P30
8. 7.P33
9. Let X and Y

Stat 200A Homework 2
(Due Wed. Oct 5 in class)
Note, the Problems and Theoretical Exercises are listed in separate sections at the end of the chapter.
1. Chapter 2, Problem 52
2. Chapter 2, Theoretical Exercise 11
3. Chapter 2, Theoretical Exercise 20
4.

STA 200A: Homework 7
Due Wed. Nov. 9
Note: Below the notation 3.T11 means Chapter 3, Theoretical Exercise 11. Similarly, the notation 4.P21
means Chapter 4, Problem 21.
1. 6.P15
2. 6.P20
3. 6.P22
4. 6.P44
5. 6.P48
6. 6.T11
7. 6.T25
8. 6.T31
9. Let X and Y