Statistics 130A
Midterm 1, version A
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Statistics 130A
Midterm 2, version A
SOLUTIONS
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STA 130A - Fall 2015 - Midterm 1
October 16, 2015
Please write your name and ID number on the test sheet. There are 50 total points. You must
Show your work to receive credit. Read each part of each question carefully. T
Statistics 130A
F. J. Samaniego
Homework # 2
Due Friday, October 9
From the text: Chapter 2 (pp. 48 51) #s 3.3, 3.11, 3.15;
Chapter 2 (pp. 55 59) #s 4.7, 4.13, 4.15.
Also, solve the following problems:
1. You give a friend a letter to mail. He forgets to
Statistics 130A
F. J. Samaniego
Homework # 1
Due Friday, October 2, 2009
From the text: Chapter 1: # 2.9, 2.11, 2.13; Chapter 2: # 1.3, 1.5, 1.9.
Also, solve the following problems:
1. Prove the Bonferroni Inequality: For any group of sets cfw_Ai : i = 1,
HOMEWORK-1 SOLUTIONS
STA-130A, FALL 2105
1. (Problem 2, Page 27) Two six-sided dice are thrown sequentially, and
the face values that come up are recorded.
(a) The sample space is:
= cfw_(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2,
HOMEWORK-2 SOLUTIONS
STA-130A, FALL 2015
1. (Problem 2, Page 64) An experiment consists of throwing a fair coin
four times. Find the frequency function and the cumulative distribution function
of the following random variables:
(a) the number of heads bef
26
Chapter 1
Probability
matches is much larger than would be expected by chance alone. This requires a
chance model; a simple one stipulates that the nucleotide at each site of fragment 1
occurs randomly with probabilities p A1 , pG1 , pC1 , pT 1 , and t
HOMEWORK-8 SOLUTIONS
STA-130A, FALL 2015
1. (Problem 35, Page 245) A simple random sample of a population of
size 2000 yields the following 25 values:
104
109
111
109
87
86
80
119
88
122
91
103
99
108
96
104
98
98
83
107
79
87
94
92
97
(a) Calculate an un
64
Chapter 2
Random Variables
2.4 Concluding Remarks
This chapter introduced the concept of a random variable, one of the fundamental
ideas of probability theory. A fully rigorous discussion of random variables requires
a background in measure theory. The
7.7 Problems
239
assumption is that of nonresponse. Response levels of only 60% to 70% are common
in surveys of human populations. The possibility of substantial bias clearly arises if
there is a relationship of potential answers to survey questions to th
312
Chapter 8
Estimation of Parameters and Fitting of Probability Distributions
way. We have data x that we regard as being generated by a probability distribution
F(x| ), which depends on a parameter . We wish to know Eh(X, ) for some
function h( ). For
Guidelines for Midterm 1
Please arrive at the exam on time or early. This will help us distribute the exams more eciently
and start on time.
The exam will be out of 100 points. The scores will be evaluated in a relative way, depending on how
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Chapter 5
Limit Theorems
size of the particle is Y1 = X 1 y0 ; after the second impact, the size is Y2 = X 2 X 1 y0 ;
and after the nth impact, the size is
Then
Yn = X n X n1 X 2 X 1 y0
n
log Yn = log y0 +
log X i
i=1
and the central limit theorem app
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EX. A {Mr Coin 2:7 Tossecl ‘0000 ﬁnes .
66 Stochastic Modeling and Mathematical Statistics
The system works if there is a path of working componepts that connects the X on the 16fI
side to the Y on the right side. The minimal “path sets, whose workmgﬁguarantees that
the system will work, are {1
The Calculus of Probability 59
6.
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12.
13.
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15.
14.
16.
Three cards are drawn at random from a 52-card deck. (a) What is the probability that
exactly two aces are drawn? (b) Assuming that you draw at least one ace and at least one
face
STA130A Midterm II Solutions
Fall, 2014. Prof. Samaniego
Updated: December 10, 2014
Problem 1
(20 points) Evaluate the expected values below, showing your detailed calculations.
a Suppose that X Be(, ) with density f (x) =
Evaluate E[X(1 X)].
(+) 1
x (1 x
Stat 130A
Answers to Sample Midterm II
Fall 2014
1. E(1/X) = 1 / ( 1).
2. k =
3 2 / 32.
)dt dx
0 x f (t=
3. EX =
t
)dx dt
0 0 f (t=
tf (t )dt
=
EX .
0
4. P(2Y > 3X) = 1/4.
5. f(y) = 6y(1 y)I(0, 1)(y); Y ~ Be(2, 2).
6.
f (u ) =
1
I (0, ) (u );
(u + 1) 2
U
Statistics 130A
F. J. Samaniego
Sample Midterm II
Fall 2014
* For discussion at Review Session, 5:10 6 PM, Dec 3, 179 Chemistry Bldg *
1.Let X ~ (, ), and assume that > 1. Find E(1/X).
2. Ive discovered a new probability model on the interval (1, 3) that
3.8 Problems
107
For example, if n = 100 and = .95, this probability is .96. In words, this means
that the probability is .96 that the range of 100 independent random variables covers
95% or more of the probability mass, or, with probability .96, 95% of a
PHP 2510
Homework 1
Due in class Oct 6
Please provide solutions to the following. In each case, show all necessary work. Report
probabilities to two or three decimal places.
1. Two six-sided dice are thrown sequentially, and the face values that come up a