Homeworks

Note that doing only the Homework examples is likely insufficient to gain practice and understanding. One learns by doing examples: this is true of all Math, but especially true of Probability. Examples other than the homework are suggested on the schedule. There are also many self-test examples in Ross (the text book).

Note also the information regarding homeworks on the Class home page.
Homeworks listed here are not final until one week before the due date. Updates made more than one week before the due date may not be notified to students.

Homework 1; Due 8.30 a.m. Wed Jan 14
Do or redo the Stat394 final exam. Here are some book sections for those who need to review,
Questions 1,2: Ross Section 3.3. Question 3: Ross Section 4.6 and 4.8.2.
Question 4(a): Ross, first part of 4.7 (P. 161); 4(c) Ross section 5.4.1.
Question 5: Ross, first part of 5.5 (P. 230-231).

Homework 2; Due 8.30 a.m. Wed Jan 21
Ross Problems: Ch 5: 1, 8, 11, 32. Ch 5: TE 8.

Homework 3; Due 8.30 a.m. Wed Jan 28
Ross Problems: Ch 5: 16, 19, 26 Ch 5: TE 9, TE 12

Homework 4; Due 8.30 a.m. Wed Feb 4
Ross Problems: Ch 6: 1(a),(b); 6, 10, 20, 21
Note: NO late homeworks this week, as solutions will be posted immediately after Wed class:
Homework 4 material will be included in the Feb 6 Midterm.

Homework 5; Due 8.30 a.m. Wed Feb 11
Ross Problems: Ch 6: 23, 27(b); 42(a); 8(a),(b); 43
Note 1: They are in this order because 8 and 43 have same setup.
(BUT be careful: Ross reverses X and Y between the two questions.)
Also, book solution is cdf not pdf; but this hwk is heavy enough that pdf is good enough for me
-- so long as you remember to say which is is!
Note 2: For 27(b), find the cdf of W = X/Y, by finding prob X/Y is less than w.

Homework 6; Due 8.30 a.m. Wed Feb 18
Ross Problems: Ch 7; 1, 3, 30&33; Ch 7; TE 18, TE 19&22.
Problems 30 and 33 count as a single question, because they are little.
Questions TE 19 and TE 22 count as a single question, because they are little.
Hint for TE 18: (posted and emailed 2/17):
N_i is the number of objects of type i. N_j is the number of objects of type j.
We have objects that are independently of types 1,2,...,i,...,j,...k with probability p_i.
What is the probability the object is of type either i or j?
So what is the pmf of the number of objects type either i or j?

Homework 7; Due 8.30 a.m. Wed Feb 25.
Ross Problems: Ch 7; 75, 21, 23, 9, 32 (n=4 only!)
Problem 75: First identify the distributions of X and Y, and then use what you know about them.
For 75 (a) I get 0.0000603 (not guaranteed!).
Problem 21: Hint: (a) Let X_i =1 if 3 people have birthday on day i, i=1,...,365.
Hint: (b) Let X_i =1 if 0 people have birthday on day i, i=1,...,365.
My answer for (b) differs slightly from the book (??); I ignored Feb 29, and assumed other days equiprobable.
Problem 9(a); Hint: show the probability urn i is empty is (i-1)/n.
Problem 9(b); Hint: if no urns are empty, where must ball n go?
Problem 32; You may solve this problem for n=4 only!!
Hint; If i is less than k, show the probability urn k is empty given i is empty is (k-2)/(n-1).

Homework 8; Due 8.30 a.m. Wed March 4.
Ross Problems: Ch 6; 2(a)&35, 3(a)&37, 28; Ch 7 Problems; 48, 51.
Problems 2(a) and 35 count as a single problem;
Problems 3(a) and 37 count as a single problem;
In Ch 7, 48/51, first find the conditional pmf/pdf.

Homework 9; Due 8.30 a.m. Wed March 11.
Ross Ch 7 Problems 40, 50, 58, Ch 7 TE 30, TE 32
No. 40,50; No integration is necessary!
Identify the pdf of X|Y, and of Y, and work with the conditional expectations given Y.
TE 30: No sums necessary!
Identify the pmf of N_i given N_j, and the marginal pmf of N_j, and work with the conditional expectations given N_j.
Generally this hwk is about avoiding computation/integration by working with the conditional pmf or pdf.