Homework set 3
Section 2.3, Problem 4. Show that F = F (x) on R has at most a countable set of points of
discontinuity. Does a corresponding result hold for distribution functions on Rn .
We rst prove the rst statement. Due to the denition of a distributi
1. Homework set 2
Section 1.8, Problem 1. Give an example of random variables and which are not independent but for which
E ( | ) = E.
(1)
Conside an unbiased die with seven faces labeled 3, 2, 1, 0, 1, 2, 3. Let be the random
variable that gives the numb
1. Homework set 1
1.1. Problem 1.2. Let contain N elements. Show that the number d(N ) of dierent decompositions of is given by the formula
d(N ) = e1
(1)
kN
.
k!
k =0
First prove the following relation:
(2)
d(N ) =
N 1
k =0
k
CN 1 d(k )
Indeed, any decom
UNIVERSITY OF CENTRAL FLORIDA
Department of Mathematics
Spring 2012
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Contents to course:
MAP6238.01 Measure and Probability
MAP 109, 4:30 p.m. - 5:45 p.m., TR
Dr. Marianna Pensky