Math 362, 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
Math 362, Problem set 4
Due 2/23/10
Note: If you turn HW in on 2/21, I will return it for you by 2/23 for the
purpose of studying for the exam.
1. (5.5.13) Let p denote the probability that, for a particular tennis player,
the rst serve is good. Since p =
Math 362, 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
Math 362, Problem set 3
Due 2/16/10
1. (5.4.18) Using the assumptions behind the condence interval given in
expression (5.4.17), show that
2
S1
S2
+ 2/
n1
n2
2
1
2
+ 2 P 1.
n1
n2
2. (5.4.24) Let X and Y be the means of two independent random samples,
each
Math 362, Problem set 2
Due 2/9/10
1. (5.2.17) Let Y1 < Y 2 < Y3 < Y4 be the order statistics of a random
sample of size n = 4 from a distribution with pdf f (x) = 2x, 0 < x < 1,
zero elsewhere.
(a) Find the joint pdf of Y3 and Y4 .
(b) Find the condition
Math 362, Problem set 5
Due 3/16/10
1. (3.7.6) Another estimating chi-square: Let the result of a random experiment be classies as one of the mutually exclusive and exhaustive ways
A1 , A2 , A3 and also as one of the mutually exclusive and exhaustive ways
Math 362, Problem set 7
Due 3/30/10
1. (6.1.11) Let X1 , . . . , Xn be a random sample from an N (, 2 ) distribution,
where 2 is xed and known, and < < .
(a) Show that the mle of is X
(b) If is restricted by 0 < , show that the mle of is =
maxcfw_0, X.
2.