# Homework, STAT 400-0201, Summer II, 2007

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. 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!).

You are welcome and encouraged to help each other in solving the problems, but for homework which is turned in, you must write your own solutions. You can examine each other's solutions. You can, I believe, buy a book with solutions to odd-numbered problems, and you can read that. BUT: when you write a solution, you must write it without copying.

You will learn the most if you work on the homework alone before consulting solutions or a classmate.

Most homework is from our text,

Jay L. Devore, Probability and Statistics for Engineering and the Sciences, 6th edition (Wadsworth, Belmont, CA, 2000).

### Homework Assignment 1 Due Wednesday July 18

Section 1.2: 17ac
Section 1.3: 33ab, 41, 42
Section 2.1: 3, 6, 9
• 9a: LHS: draw a picture of A U B, and then (A U B)';
• 9a: RHS: draw pictures of A', B' and then their intersection
• 9b: do it similarly.
Section 2.2: 11, 13, 21, 22, 26

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### Homework Assignment 2 Due Friday July 20

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 24

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
BONUS: 1 extra point for solving the hats problem.
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### Homework Assignment 4 Due Thursday, July 26

Section 3.3: 28, 32, 34, 37, 42, 43a
Section 3.4: 45-48, 51, 61
Section 3.5: 64,70

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: 77, 79, 81, 83
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### Homework Assignment 5 Due Wednesday August 1

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

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### Homework Assignment 6 Due Friday August 3

Section 4.3: 26cdj, 27abd, 29b, 30bc, 35a,37,39,51
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 8

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 10

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.]
BONUS PROBLEM (2 points)
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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 16

Section 6.1: 1abcd, 9, 13, 14
Section 6.2: 20, 22, 25a, 30, 31[just read 31], 32

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### Homework Assignment 10 Due Friday, August 17

(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 11 Due Tuesday August 21

Section 7.2: 12, 13, 15ab,17,19, 25
Section 7.3: 30acef, 32, 37a
[In 7.3: we will only cover confidence intervals,
not prediction and tolerance intervals.]

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### Homework 12 Due Wednesday August 22

Section 8.1: 1,2,9
Section 8.2: 15a, 19,28
Section 8.4: 45ad

ABOVE: for the hypothesis test questions 19, 28:
1. State null and alterate hypotheses
2. State test statistic
3. State significance level, rejection region
4. Evaluate the test statistic for the data;
5. Give your conclusion on whether the null hypothesis is
rejected, and state the meaning in terms of your actual decision.
6. Compute the P-value as in Sec. 8.4, and comment on its
meaning in terms of whether or not it gives
additional strong support for your decision.

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