Homework for Math 461

Homework will be assigned most weeks, to be handed in about a week later to my office 376 Altgeld, by 5pm on the due date.
The exercises below are not final until the due date is assigned, each week. So please check this website weekly.

Median scores on the HW are (out of 10): 8.5, 8.0, 8.5, 5 (Iprom project), 8.0, 7.5, 9.0, 8.5, 7.0, 8.0, 9.0, 4.0 (out of 5)

Median score on Test 1: 83/100 (top score 112/100)

Median score on Test 2: 66/100 (top score 107/100)

Here you can download the summary sheets on discrete densities and continuous densities.

Homework guidelines. Show all your working. Do not just give numerical answers. Write your solutions using proper English sentences wherever possible. Words like "if, then, because" are particularly helpful to the grader evaluating your solution.

Section of the book Exercise pages Exercises
1.3 16-18 7, 8c, 12, due Sep 5
1.4 16-18 19, 21, due Sep 5
1.5 16-18 29, due Sep 5
Ch. 1 theory 19-22 3, 5, 8, 9, 20, due Sep 5
2.2 55-60 2, 7 due Sep 13
2.3, 2.4 55-60 12, due Sep 13
2.5 55-60 18, 20, 21, 25, 28, due Sep 13
2.5 55-60 37, 53 (see Example 5n), 54, due Sep 13
Ch. 2 theory 61-63 8, 11, 20, due Sep 20
3.2 111-124 1, 9, 14a (see multiplication rule, p. 71), 18a due Sep 20
3.3 111-124 47 (see conditioning formula (3.4)), 50, 51, due Sep 20
3.4 Iprom Project 1, due Sep 22
3.4 111-124 56 (e.g. coupon=butterfly), 57 (Bernoulli trials!), 62, 81 (rephrase it as Gambler's Ruin), 83, due Oct 4
Ch. 3 theory 124-128 22, due Oct 4
4.1 187-197 4, due Oct 4
4.2 187-197 14, due Oct 4
4.3-4.5 187-197 20, 23 ("strategy" means buy/sell either now or at end of week or some combination of both), 27, 32 (the group of 100 is irrelevant, just consider the group of 10), 33 (write M for the number of papers the newsboy purchases, and write down a formula for his expected profit, then use a computer to evaluate for the possible values of M), 38, due Oct 11
4.6 187-197 46 (after you get a formula, evaluate by computer), 48, due Oct 11
4.7 187-197 55, 56 (use Poisson approximation to Binomial), 57, 60, 70 (note: if you did not know the first flip came up heads, then the answer would just be p), due Oct 18
4.8 187-197 73 (World Series!), due Oct 18
4.9 187-197 17 (first sketch the graph of F(b)), due Oct 18
Ch. 4 theory 197-201 5, 9, 13, 18 (and discuss the relation to #13), due Oct 18
5.1 247-251 1 (first graph f(x)), 4, 5, due Oct 26
5.2--5.3 247-251 6a, 12, due Oct 26
5.4 247-251 16, 18, 22, 28 (Normal Approximation), 24, due Oct 26
5.5 247-251 32, 33, 34 (and how close are the answers to (a) and (b)?), due Oct 26
5.6--5.7 247-251 39, 41, due Nov 10
6.1 313-319 2a, 7, due Nov 10
6.2 313-319 13, 14, 21, due Nov 10
6.3 313-319 27, 32, 34, due Nov 10
6.4-6.6 313-319 41, 42 (but in (a), don't find the conditional density of X given Y), 45, 49(b), 51, due Nov 17
Ch. 6 theory 319-322 18(b) (and identify your answer in terms of a standard distribution), 24 (assume L=1, and do the cases n=2, n=3; for extra credit, do the case of arbitrary n), due Nov 17
7.2 408-418 5, 7(a), 8, Extra credit: 11, due Nov 17
7.2 408-418 19, 21 (in part (b), you're counting the number of days of the year that are someone's birthday), 25 (remarkable because the answer does not depend on the type of the random variable), due Dec 1
7.4 408-418 30 (explain where you use independence), 38 (the Gamma function helps simplify your calculations), 39 (use linearity of covariance, from Prop. 3.2(iv)), 41 (do it two ways: (a) hypergeometric, and (b) writing X=X1+...+X30), 42 (first part only), due Dec 1
7.5 408-418 57 (see Example 5d in Section 7.5), 56 (condition on number of passengers), 55 (condition on number of ducks), due Dec 6
7.7 408-418 75bc, not due (exam preparation)
8.2 457-459 1, 2ab, not due (exam preparation)
8.3 457-459 5, not due (exam preparation)


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