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 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 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 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 9
Due 11/1/10
1. (2.2.3) Let X1 and X2 have the joint pdf h(x1 , x2 ) = 2ex1 x2 , 0 < x1 <
x2 < , zero elsewhere. Find the joint pdf of Y1 = 2X1 and Y2 = X2 X1 .
2. (2.3.2) Let f1|2 (x1 |x2 ) = c1 x1 /x2 , 0 < x1 < x2 , 0 < x2 < 1 ze
Math 361, Problem Set 2
October 26, 2010
Due: 11/1/10
1. (2.1.5) Given that the nonnegqative function g(x) has the property that
g(x)dx = 1, show that
0
f (x1 , x2 ) =
2g( x2 + x2 )
1
2
x2 + x2
1
2
,
0 < x1 <
0 < x2 < ,
zero elsewhere, satises the condit
Math 361, Problem set 11
Due 11/6/10
1. (3.4.32) Evaluate
appendix table.
3
2
exp(2(x 3)2 )dx - without a calculator. Use the
2. (3.4.19) Let the random variable X have a distribution that is N (, 2 ).
(a) Does the random variable Y = X 2 also have a norm
Math 361, Problem set 9
Due 11/8/10
1
1. (2.5.3) Let p(x1 , x2 ) = 16 , x1 = 1, 2, 3, 4 and x2 = 1, 2, 3, 4, zero elsewhere,
be the joint pmf of X1 and X2 . Show that X1 , X2 are independent.
2. (2.5.8) Let X and Y have the joint pdf f (x, y) = 3x, 0 < y
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 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 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