Homework, STAT 400-0201, Summer II, 2008

Note! For every section in the text we cover -- the main part of your homework is to read that section.

Homework is due in class on the day listed. No late homework will be accepted. It is OK to work on the problem sets in cooperation with others, but you must write up the solutions by yourself. . Your solutions should give a clear indication of how you came to your answers (especially when the answer is in the back of the text!).

Sections numbers and Homework numbers are from the Textbook

Jay L. Devore, Probability and Statistics for Engineering and the Sciences, 7th edition (ISBN: 978-0-4-9540049-3)

Homework Assignment 1
Due Wednesday July 16

Section 1.2: 17ac
Section 1.3: 33ab, 41, 42
Section 2.1: 2, 3, 6, 9 Section 2.2: 11, 13, 21, 22, 26

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Homework Assignment 2
Due Friday July 18

Section 2.3: 33, 34, 36, 40, 43, 44
Ch. 2 Supplementary exercises: 103ab
Section 2.4: 45, 46, 51, 60, 62, 64

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Homework Assignment 3
Due Tuesday July 22

Section 2.5: 72, 75, 78
Ch. 2 Supplementary excercises: 98, 99
Section 3.1: 2, 7
Section 3.2: 11, 12a, 13, 14a, 15, 18, 23
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Homework Assignment 4
Due Thursday, July 24

Section 3.3: 29, 32, 34, 37, 42, 44a
Section 3.4: 46-48, 51, 61
Section 3.5: 68,70

BONUS Problem A:
Joe will roll a pair of dice until he rolls a 7 (i.e., the numbers on the two dice sum to 7).
Let X be the number of times he will roll without getting a 7.
(For example, if on the third roll Joe first rolls 7, then X=2.)
What is the expected value of X?

[Hint for Problem A: Let p(x) denote the probability that X=x.
The expected value will be an infinite series, (0)p(0) + (1)p(1) + (2)p(2) + (3)p(3) + ... .
After you determine the formula for p(n), to compute the series recall
1 + x + x^2 + x^3 + ... = 1/(1-x), if |x|<1.
Now take the derivative of both sides.]

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Section 3.6

(Do not turn this assignment in; however a related problem will be on Exam 1.)
Section 3.6: 79, 81, 83
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Homework Assignment 5
Due Wednesday July 30

Section 4.1: 1, 2, 7
Section 4.2: 11, 18, 21, 23

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Homework Assignment 6
Due Friday August 1

Section 4.3: 28cdj, 29abd, 30b, 31bc, 35a,37,39
Section 4.4: 59, 61, 63
    (In Section 4.4, we will only cover the exponential distribution.)

BONUS PROBLEM (1 point): Suppose X is a normal random variable
with mean mu and standard deviation sigma, and we have numbers
a,b with a less than b. By definition, Prob (mu + (a)sigma < X < mu + (b)sigma)
is the integral of the p.d.f. for this distribution over the interval from
mu + a(sigma) to mu + b(sigma). Use a change of variables to show that this
definite integral equals the definite integral of the p.d.f. for the standard
normal distribution over the interval from a to b.

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Homework Assignment 7
Due Wednesday August 6

As always, show enough work to reveal the logic behind your numerical answer,
especially when the answer is in the back of the book.

Section 5.1: 3, 4, 10, 12, 13, 15, 17
    (Hint. 10bc: the events correspond to certain regions in the square.
    Draw the square and regions and compute the areas.)
Section 5.2: 24, 25

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Homework Assignment 8
Due Friday, August 8

Section 5.2: 27, 35
(Hint. In #27, to compute the appropriate integral involving |X-Y|, split the square into pieces where X-Y is positive or negative.)
Section 5.3: 38
Section 5.4: 46, 47, 53 [In #53b, do not assume the hardness of pins has a normal distribution, and justify the approximation.]
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Section 5.5

59, 64 69 (Do not turn this assignment in; however a related problem will be on Exam 2.)

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Homework Assignment 9
Due Thursday, August 14

Section 6.1: 1abcd, 9, 13, 14

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Homework Assignment 10
Due Friday, August 15


Section 6.2: 20, 22, 25a, 30, 31[just read 31], 32
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Homework 11
Due Tuesday August 19

(Remember to show enough work that the grader can follow your logic.)
Section 7.1: 1bd, 2, 3, 4abe, 7, 11

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Homework 12
Due Wednesday August 20


Section 7.2: 12, 13, 15ab,17,19, 25
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