Math 493 - Homework

# Homework

## Suggested study problems on the LLN and CLT

Consider doing the following problems from the textbook:

## Homework 12, due Dec 10 at 2:07pm

Please do the following problems from the textbook:

A.  Show that if X and Y are Poisson random variables, with parameters a and b, respectively, then X + Y is Poisson with parameter a + b.

## Homework 11, due Dec 1 at 2:07pm

Please do the following problems from the textbook:

Grinstead-Snell, p263: 4, 12, 15, 18, 30 (see below)

A.  Show that if X is a continuous random variable with Riemann density function f, then E( cX ) = cE( X ).
(I.e., show that part of linearity of expectation holds for continuous random variables.)

Note: Depending on what version of the book you have, p263 30 may be p263 29. It is to calculate the variance of a Poisson random variable.

## Homework 10, due Nov 17 at 2:07pm

Please do the following problems from the textbook:

Grinstead-Snell, p247: 4, 6, 11, 36

## Homework 9, due Nov 10 at 2:07pm

Please do the following problems from the textbook:

## Homework 8, due Nov 3 at 2:07pm

Please do the following problems from the textbook:

Grinstead-Snell, p172: 1, 2, 6, 8, 9

## Homework 7, due Oct 27 at 2:07pm

Please do the following problems from the textbook:

Grinstead-Snell, p150: 12, 15, 22, 26, 32, 39, 46, 54

Note: a bridge hand (as in problem 15) has 13 cards.

## Homework 6, due Oct 20 at 2:07pm

Please do the following problems from the textbook:

Grinstead-Snell, p150: 2, 4, 6, 8, 17, 63

A.  Let m(w) be a uniform discrete probability distribution, and E be an event with P(E) > 0. Show that m( w | E ) is a uniform discrete probability distribution.

Graded were p131: 1, and p160: 4, 8, 17.

## Homework 5, due Oct 13 at 2:07pm

Please do the following problems from the textbook:

Grinstead-Snell, p115: 18, 29, 34a, 36

Note: you'll have to work hard for #36!

Graded were p115: 29, 34a, 36a, and 4.

## Homework 4, due Oct 8 at 2:07pm

Please do the following problems from the textbook:

Grinstead-Snell, p115: 6, 7, 10, 26

## Homework 3, due Sep 29 at 2:07pm

Please do the following problems from the textbook:

Grinstead-Snell, p88: 3, 6, 10, 11, 16, 23

A.  Prove the identity in Problem 35 on p118 by examining the coefficient of xn in ( 1 + x )2n.

Graded were p88: 11, 16; p115: 20; and Problem A.

## Homework 2, due Sep 22 at 2:07pm

Please do the following problems from the textbook:

Grinstead-Snell, p71: 2, 3, 4, 8, 12, 14, 15, 16

Graded were p71: 2, 4, 12, 15.

## Homework 1, due Sep 15 at 2:07pm

Please do the following problems from the textbook: