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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