School of Engineering and Applied Science
The George Washington University
ECE 6015
Stochastic Processes in Engineering
Homework #3 Solutions
Problem 1
4.12)
(b) P[x<=1]=.5
P[x=1]=.5
P[x<.5]=P[x<=.5
School of Engineering and Applied Science
The George Washington University
ECE 6015
Stochastic Processes in Engineering
Homework #12 Solutions
Problem 1
11.1)
a)Mn=1/n
=1/n[xn+(n1)Mn1]=1/n xn+(11/n
School of Engineering and Applied Science
The George Washington University
ECE 6015
Stochastic Processes in Engineering
Homework #8 Solutions
Problem
9.2)
(a) is
If =1:
If =2:
.
.
If =6:
1
the output
School of Engineering and Applied Science
The George Washington University
ECE 6015
Stochastic Processes in Engineering
Homework #10 Solutions
Problem 1
10.1)
a)SX(f)=F[g(
=AT
Table in Appendix B
b) S
School of Engineering and Applied Science
The George Washington University
ECE 6015
Stochastic Processes in Engineering
Homework #11 Solutions
Problem 1
10.27)
a)Syx(f)=H(f)Sx(f)=
Rxy=
[Syx(f)]=
b)Sy(
School of Engineering and Applied Science
The George Washington University
ECE 6015
Stochastic Processes in Engineering
Homework #9 Solutions
Problem 1
9.37)
a)pcfw_T1<T2=
=
b)f1(t)=
dt=
=2/3
f2(t)=
F
School of Engineering and Applied Science
The George Washington University
ECE 6015
Stochastic Processes in Engineering
Homework #6 Solutions
Problem 1
5.48)
(a) P[ <1/2, y<1/2]= P[
<1/2] P[y<1/2]
School of Engineering and Applied Science
The George Washington University
ECE 6015
Stochastic Processes in Engineering
Homework #4 Solutions
Problem 1
4.48)
E[
=
]=
dx
= 
 +
= 
 + (
VAR[x]=

u=
School of Engineering and Applied Science
The George Washington University
ECE 6015
Stochastic Processes in Engineering
Homework #2 Solutions
Problem 1
2.26) Identities of this type are shown by appli
School of Engineering and Applied Science
The George Washington University
ECE 6015
Stochastic Processes in Engineering
Homework #1 Solutions
Problem 1
2.2) The output of this experiment consists of a
School of Engineering and Applied Science
The George Washington University
ECE 6015
Stochastic Processes in Engineering
Homework #5 Solutions
Problem 1
5.20)
(b) FX(x)= Fxy(x,)= 1
x>1
0
otherwise
Fy(
School of Engineering and Applied Science
The George Washington University
ECE 6015
Stochastic Processes in Engineering
Homework #7 Solutions
Problem 1
7.1)
(a)E[x+y+z]=E[x]+E[y]+E[z]=0
VAR[x+y+z]=VAR