Math 510 HW #22
Due 11/25
Problem 1 Ch. 9 Theo. ex. p. 484 #1, 2, 3
Problem 2 Suppose N (t) is a Poisson process with = 2. Find:
a. P (N (2) = 3)
b. P (N (10) N (7) = 4)
c. P (N (10) N (7) = 4 | N (2) = 3)
d. P (N (5) N (2) = 4 | N (3) = 1). Hint: Split t
Math 510 HW #21
Due 11/21
Problem 1 Ch. 8 Problems p. 457 #3, 4, 5, 6, 7, 8, 13
Problem 2 In this and the next several problems, we will explore why we used
4
Sn in the proof of the strong law of large numbers.
2
2
Why couldnt we use Sn in the proof ? Wor
Math 510 HW #20
Due 11/18
Problem 1 Let X1 , . . . , Xn be independent, identically distributed (i.i.d.) random variables, each with expected value 3 and standard deviation 7.
Find the expected value and standard deviation of X = X1 +Xn .
n
Problem 2 In t
Math 510 HW #23
Due 12/2
Problem 1 Ch. 9 p. 484, problems #4, 5, 6, 9, 10
Problem 2 Let U be a uniform (0,1)
1
2
X=
3
4
random variable. Dene X as follows:
U < .2
.2 U < .4
.4 U .6
U > .6
(a) Give the mass function for X. (b) Give the cumulative distrib
Math 510 HW #19
Due 11/11
Problem 1 Let X be a random variable with the following mass distribution:
0
1
2
.3
.5
.2
Find the moment generating function for X.
Problem 2 Let X be a random variable with the density function
f (x) =
x, 0 < x < 1
0, otherwise