Math 361, Problem Set 1
August 27, 2010
1. (1.2.9) If C1 , C2 , C3 , . . . are sets such that Ck Ck+1 , k = 1, 2, 3, . . . , , we dene limk Ck as the intersection k=1 Ck = C1 C2 . . . . Find limk Ck for the following, and draw a picture of a typical Ck on

Midterm Exam I
Math 361 9/27/10 Name: Read all of the following information before starting the exam: READ EACH OF THE PROBLEMS OF THE EXAM CAREFULLY! Show all work, clearly and in order, if you want to get full credit. I reserve the right to take o point

Midterm Exam I
Math 361 9/27/10 Name: Read all of the following information before starting the exam: READ EACH OF THE PROBLEMS OF THE EXAM CAREFULLY! Show all work, clearly and in order, if you want to get full credit. I reserve the right to take o point

Math 361, Problem set 7
Due 10/25/10 1. (1.9.6) Let the random variable X have E[X ] = , E[(X )2 ] = 2 and mgf M (t), h < t < h. Show that E and E exp t X = et/ M t , h < t < h. X = 0, E X
2
=1
(Recall: exp(x) = ex ). 2. (1.9.7) Show that the moment gene

Math 361, Problem set 6
Due 10/18/10 1. (1.8.3) Let X have pdf f (x + 2)/18 for 2 < x < 4, zero elsewhere. Find E[X ], E[(X + 2)3 ] and E[6X 2(X + 2)3 ]. 2. (1.8.5) Let X be a number selected uniformly random from a set of numbers cfw_51, . . . , 100. App

Math 361, Problem set 5
Due 10/04/10 1. (1.6.8) Let X have the pmf p(x) = ( 1 )x , x = 1, 2, 3, . . . , and zero else2 where. Find the pmf of Y = X 3 . Answer: Y has pmf p(x) = ( 1 )x/3 for x = 1, 8, 27, . . . , and zero elsewhere. 2 2. (a) Pick a card fr

Math 361, Problem set 5
Due 10/04/10 1. (1.6.8) Let X have the pmf p(x) = ( 1 )x , x = 1, 2, 3, . . . , and zero else2 where. Find the pmf of Y = X 3 . 2. (a) Pick a card from a standard deck. Let X denote the rank of the card(counting ace as one, J=11, Q

Math 361, Problem set 4
Due 9/27/10 1. (1.4.26) Person A tosses a coin and then person B rolls a die. This is repeated independently until a head or one of the numbers 1, 2, 3, 4 appears, at which time the game is stopped. Person A wins with the head, and

Math 361, Problem set 4
Due 9/20/10 1. (1.4.26) Person A tosses a coin and then person B rolls a die. This is repeated independently until a head or one of the numbers 1, 2, 3, 4 appears, at which time the game is stopped. Person A wins with the head, and

Math 361, Problem set 3
Due 9/20/10 1. (1.4.21) Suppose a fair 6-sided die is rolled 6 independent times. A match occurs if side i is observed during the ith trial, i = 1, . . . , 6. (a) What is the probability of at least one match during on the 6 rolls.

Math 361, Problem set 3
Due 9/20/10 1. (1.4.21) Suppose a fair 6-sided die is rolled 6 independent times. A match occurs if side i is observed during the ith trial, i = 1, . . . , 6. (a) What is the probability of at least one match during on the 6 rolls.

Math 361, Problem Set 2
September 17, 2010
Due: 9/13/10 1. (1.3.11) A bowl contains 16 chips, of which 6 are red, 7 are white and 3 are blue. If four chips are taken at random and without replacement, nd the probability that (a) each of the 4 chips is red

Math 361, Problem Set 2
September 3, 2010
Due: 9/13/10 1. (1.3.11) A bowl contains 16 chips, of which 6 are red, 7 are white and 3 are blue. If four chips are taken at random and without replacement, nd the probability that (a) each of the 4 chips is red

Math 361, Problem Set 1 Solutions
September 10, 2010
1. (1.2.9) If C1 , C2 , C3 , . . . are sets such that Ck Ck+1 , k = 1, 2, 3, . . . , , we dene limk Ck as the intersection k=1 Ck = C1 C2 . . . . Find limk Ck for the following, and draw a picture of a

Midterm Exam I
Math 361 9/27/10 Name: Read all of the following information before starting the exam: READ EACH OF THE PROBLEMS OF THE EXAM CAREFULLY! Show all work, clearly and in order, if you want to get full credit. I reserve the right to take o point