Stochastic Process
Fall 2014
Assignment 3
TSUNG-HSIEN LI()
R01323016 [at] ntu.edu.tw
Exercise 2.46
(a) Following the hint, we know that
X = In ,
n=1
where
1 if n X,
In =
0 if n > X.
Therefore,
n=1
n=1
E(X) = E(I n ) = P(X n).
In addition, letting m = n
Stochastic Process
Fall 2014
Assignment 2
TSUNG-HSIEN LI()
R01323016 [at] ntu.edu.tw
Binomial Distribution
- Moment generation function
n
n
(t) = E(e tx ) = C x (pe t )x (1 p)nx = (pe t + (1 p)n .
x=0
- Mean
E(x) = (t)
t=0
= npe t (pe t + (1 p)n1
t=0
= np
Stochastic Process
Fall 2014
Assignment 1
TSUNG-HSIEN LI()
R01323016 [at] ntu.edu.tw
Exercise 1.8
First, we know that by (1.2)
P(E F) = P(E) + P(F) P(E F),
and P(E F) must be less than one. Then,
P(E F) = P(E) + P(F) P(E F)
P(E) + P(F) 1.
Hence, we compl