EE 605
Probability & Stochastic Processes 1
Fall 2016
Homework 2
Problem 1
Trains X and Y arrive at a station at random between 10:00 am and 10:20 am. Train X stops for
4 minutes at the station, and train Y stops for 5 minutes. Trains arrive independently
EE 605 Probability and Stochastic Processes I
MIDTERM EXAM - Solutions
Problem 1
Solution
(20 points) A die is rolled until the first time T that a six comes up.
a) Find the probability distribution for the random variable T.
b) Find P(T > 3).
c) Find P(T
Problem
Given two independent random variables, X and Y, with probability densities
1
2
()
= cfw_2 ,
0,
0
<0
1
2,
()
= cfw_2
0,
0
<0
Find the probability density of the random variable Z = X + Y.
Solution
2, 0
() = cfw_4
0, < 0
Problem
Random varia
Problem
Joint pdf of RVs X and Y is defined as
, 2 + 2 1
, (, ) = cfw_
0, otherwise
a) Find the constant c.
b) Find marginal pdfs and expected values of RVs X and Y
c) Find Ecfw_XY
Solution
1
a) = since
1 = , (, ) =
and domain D: 2 + 2 1
b)
12
() = , (,
EE 605
Probability & Stochastic Processes 1
Fall 2016
Homework 2 - Solutions
Problem 1
Trains X and Y arrive at a station at random between 10:00 am and 10:20 am. Train X stops for
4 minutes at the station, and train Y stops for 5 minutes. Trains arrive i
EE 605
Probability & Stochastic Processes 1
Fall 2016
Homework 1 - Solution
Problem 1
When three dice are rolled, gamblers noticed that the sum of their faces equal to 9 comes
somewhat less often than the sum of faces equal to 10.
a) Write a program to si
Name: Shen Liu
1.A:
2.A:
EE605
a) P(X arrives before Y)=P(X<Y)=1/2
b) A = cfw_X arrives in (t1,t2)=cfw_t1<=X<=t2, B=cfw_Y arrives in (t3,t4)=cfw_t3<=Y<=t4
P(A) = 4/20, P(B)=5/20, A&B are independent
So, P(AB)=P(A)*P(B)=4/20*5/20=1/20
c) C = cfw_trans met
EE 605
Probability & Stochastic Processes 1
Fall 2016
Homework 1
Problem 1
When three dice are rolled, gamblers noticed that the sum of their faces equal to 9 comes
somewhat less often than the sum of faces equal to 10.
a) Write a program to simulate this
Name: Shen Liu
Homework 1
EE605
A1:
a) Package w1;
Public class Ew(
Public static void main(String[] args)cfw_
int []a= new int [100050];
int count1=0;
int count2=0;
for (int i=0;i<=100000;i+)cfw_
int n1=(int)(Math.random()*6+1);
int n2=(int)(Math.random(
Stevens Institute of Technology Dept. ECE
EE603 Linear System Theory
Lecture 5
Instructor: Rensheng Wang
Department of Electrical and Computer Engineering
Stevens Institute of Technology Dept. ECE
Ch4. Continuous-Time Fourier Transform
Stevens Institute o