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1.
A survey of a groups viewing habits over the last year revealed the following
information:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
28% watched gymnastics
29% watched baseball
19% watched soccer
14% watched gymnastics and baseball
12% watched b
Math 280B, Winter 2012
Homework 4
1. Problem 3 (page 261)
2. Problem 6 (page 261)
3. Problem 13 (page 262)
4. Problem 21 (page 263)
5. Let X1 , X2 , . . . be random variables, such that Xn has the Poisson distribution with
parameter n > 0. Suppose that li
Math 280B, Winter 2012
Homework 3
1. Problem 1 (page 197) (The exponential random variables Y1 and Y2 are to have parameter 1.)
2. Problem 4 (page 197)
3. Problem 6 (page 197)
4. Let X and Y be independent standard normal random variables. Show that
X +Y
Math 280B, Winter 2012
Homework 1
1. Problem 5 (page 261)
2. Problem 7 (page 261)
3. Problem 20 (page 263)
4. For each n = 1, 2, . . . let Xn be uniformly distributed over the nite set cfw_1, 2, . . . , n.
That is,
P[Xn = k] =
1
,
n
k = 1, 2, . . . , n.
S
Math 280B, Winter 2012
Homework 2
1. Problem 4 (page 261)
2. Problem 14 (page 262)
d
3. Suppose that Xn X and that supn E |Xn |2+ < for some > 0. Show that (a)
2
E[X 2 ] < (so that E[|X|] < ), (b) limn E[Xn ] = E[X] and (c) limn E[Xn ] = E[X 2 ].
4. Let X