EL 6303, Probability and Stochastic Processes
Fall 2016
Elza Erkip
EXERCISE SET-V SOLUTIONS
1.
1.
2.
3. (a)
(b)
4.
October 7, 2016
2. Lets discuss a more general problem.
1
k
p 1 p p2 . 1 p . Differentiating both sides with respect to p, we get
k 0
kp
k
EL 6303, Probability and Stochastic Processes
Fall 2016
Elza Erkip
October 7, 2016
EXERCISE SET-V
1.
2. Let
P( X k ) Bkp k 1, k 1,2,., ; 0 p 1.
(a) Find B so that
P( X k ) represents a probability mass function.
(b) Find
Ecfw_X .
(c) Find
Ecfw_X 2.
(d) Fi
EL 6303, Probability and Stochastic Processes
Fall 2016
Elza Erkip
EXERCISE SET-VIII SOLUTIONS
1.
November 10, 2016
2. The following solution uses the term Transform which is another name for
moment generating function.
3.
4.
5.
6.
7.
8.
9.
1.
2. a)
b)
c)
Generalized Bernouli Trials
Consider the collection of all possible sequences of As, Bs and
Cs, in which there are 3 As, 2 Bs, and 5Cs. Two examples of
such sequences are shown below.
ACABCCBACC
CBABAACCCC
We want to answer the question, how many differen