ECE 250 Random Processes
Homework 1
1. The random variable X has the density
e x ,
f X (x)
0,
x0
x 0.
A new random variable is given by
Y e X . Obtain an expression for the n-th moment of Y.
2. Can
UCSD ECE153
Prof. Young-Han Kim
Handout #7
Wednesday, January 21, 2015
Weekly Exercise Set #3
1. Let A be a nonzero probability event A. Show that
(a) P(A) = P(A|X x)FX (x) + P(A|X > x)(1 FX (x).
P(A|
ECE 35
Lab Report 3
Lab Section #: A50
Monday 8:30 AM - 11:30 AM
Tengda Li
PID: A11950705
Yuankai Le
PID: A91408854
Introduction:
The objective of this lab is to design and build an analog optical dat
UCSD ECE250
Prof. Young-Han Kim
Handout #11
Wednesday, February 4, 2015
Exercise Set #5
1. Neural net. Let Y = X + Z, where the signal X U[1, 1] and noise Z N(0, 1) are
independent.
(a) Find the funct
UCSD ECE250
Prof. Young-Han Kim
Handout #10
Wednesday, February 4, 2015
Solutions to Exercise Set #4
(Prepared by TA Fatemeh Arbabjolfaei)
1. Two envelopes. An amount A is placed in one envelope and t
UCSD ECE250
Prof. Young-Han Kim
Handout #18
Wednesday, March 4, 2015
Exercise Set #7
1. Symmetric random walk. Let Xn be a random walk dened by
X0 = 0,
n
Xn =
Zi ,
i=1
1
where Z1 , Z2 , . . . are i.i.
UCSD ECE250
Prof. Young-Han Kim
Handout #17
Wednesday, March 4, 2015
Solutions to Exercise Set #6
(Prepared by TA Fatemeh Arbabjolfaei)
1. Linear estimator. Consider a channel with the observation Y =
UCSD ECE250
Prof. Young-Han Kim
Handout #14
Wednesday, February 11, 2015
Midterm Examination
(Total: 100 points)
There are 4 problems, each problem with multiple parts, each part worth 10 points. Your
UCSD ECE250
Prof. Young-Han Kim
Handout #16
Wednesday, February 18, 2015
Exercise Set #6
1. Linear estimator. Consider a channel with the observation Y = XZ, where the signal X and
2
the noise Z are u
UCSD ECE250
Prof. Young-Han Kim
Handout #19
Wednesday, March 11, 2015
Solutions to Exercise Set #7
(Prepared by TA Fatemeh Arbabjolfaei)
1. Symmetric random walk. Let Xn be a random walk dened by
X0 =
UCSD ECE250
Prof. Young-Han Kim
Handout #12
Monday, February 9, 2015
Solutions to Exercise Set #5
(Prepared by TA Fatemeh Arbabjolfaei)
1. Neural net. Let Y = X + Z, where the signal X U[1, 1] and noi
UCSD ECE250
Prof. Young-Han Kim
Handout #13
Monday, February 9, 2015
Midterm Review
(Prepared by TA Fatemeh Arbabjolfaei)
1. Order statistics.
Let X1 , X2 , X3 be independent and uniformly drawn from
UCSD ECE250
Prof. Young-Han Kim
Handout #22
Wednesday, February 18, 2015
Solutions to Final Examination
(Prepared by TA Fatemeh Arbabjolfaei)
1. Drawing balls without replacement (20 pts). Suppose tha
UCSD ECE250
Prof. Young-Han Kim
Handout #21
Wednesday, February 18, 2015
Final Examination
There are 6 problems, each problem with multiple parts, each part worth 10 points. Your answer
should be as c
ECE 250 Midterm
November 3, 2017
SOLUTION
1. The random variables X and Y have the joint density
fx,y(x,y) = ~(x + y)e-Cx+y),O < x,y
Determine the density of Z = X
< oo.
+ Y.
An answer not supported b
ECE 250 Midterm
October 28, 2016
SOLUTION
1. The discrete random variable X has the probabilities
P(X = -2) = P(X = -1) = P(X = 1) = P(X = 2) = 1/4.
The random variable Y is defined by Y =
independent
HW3
Shahar Dror
Question 1
Because the distribution of X , Y are the same, we can calculate the moments of X for both random variables:
EX
1
0
1
1
1
0
1
0
0
x 2 x3
2 3
xf X x dx x 1 x dx x 1 x dx x 1
UCSD ECE250
Prof. Young-Han Kim
Handout #3
Wednesday, January 7, 2015
Weekly Exercise Set #1
1. Using the axioms of probability, show that A B implies that P(A) P(B).
2. Independence. Show that the ev
UCSD ECE250
Prof. Young-Han Kim
Handout #9
Wednesday, January 28, 2014
Exercise Set #4
1. Two envelopes. An amount A is placed in one envelope and the amount 2A is placed in
another envelope. The amou
UCSD ECE250
Prof. Young-Han Kim
Handout #5
Wednesday, January 14, 2015
Weekly Exercise Set #2
1. Jurors fallacy. Suppose that P(A|B) P(A) and P(A|C) P(A). Is it always true that
P(A|B, C) P(A) ? Prove
UCSD ECE250
Prof. Young-Han Kim
Handout #6
Wednesday, January 21, 2015
Solutions to Exercise Set #2
(Prepared by TA Fatemeh Arbabjolfaei)
1. Jurors fallacy. Suppose that P (A|B) P (A) and P (A|C) P (A
UCSD ECE250
Prof. Young-Han Kim
Handout #4
Wednesday, January 14, 2015
Solutions to Exercise Set #1
(Prepared by TA Fatemeh Arbabjolfaei)
1. Using the axioms of probability, show that A B implies that
UCSD ECE 250
Prof. Young-Han Kim
Handout #8
Wednesday, January 28, 2015
Solutions to Exercise Set #3
(Prepared by TA Fatemeh Arbabjolfaei)
1. Let A be a nonzero probability event. Show that
(a) P(A) =
UCSD ECE250
Prof. Young-Han Kim
Handout #20
Wednesday, March 11, 2015
Final Review
(Prepared by TA Fatemeh Arbabjolfaei)
1. Random-delay mixture.
Let cfw_X(t), < t < , be a zero-mean wide-sense statio
ECE 250 Midterm
November 7, 2014
SOLUTION
1. Let Xk, k = 1, 2, . , be independent and identically-distributed with common density
fx(x)=cfw_e-x, x>O
O,x<O
ConsiderthesumZn
ixk.
=
k=I
ElX)o.J = S~ ~ t
ECE 250 FALL QUARTER 2015
ELECTRICAL & COMPUTER ENGINEERING
Course:
ECE 250 Random Processes
URL:
https:/sites.google.com/a/eng.ucsd.edu/ece-250-f2015/
Text:
H. Stark & J. W. Woods, Probability and Ra
UCSD ECE250
Prof. Young-Han Kim
Handout #6
Wednesday, January 21, 2015
Solutions to Exercise Set #2
(Prepared by TA Shouvik Ganguly)
1. Jurors fallacy. Suppose that P (A|B) P (A) and P (A|C) P (A). Is
UCSD ECE 250
Prof. Young-Han Kim
Handout #8
Wednesday, January 28, 2015
Solutions to Exercise Set #3
(Prepared by TA Shouvik Ganguly)
1. Nonlinear processing. Let X Unif [1, 1]. Define the random vari
Final Examination
December 5, 2016
SOLUTION
1. The random variable X has the probability density
1
fx (x) =
n(l + x2), -oo < x < oo.
Determine the probability density of Y =
_!_,
X
An answer not suppo
250 Random Processes
Homework 4
1. The input, X(t), and output, Y(t), of a linear system are related via the differential equation
If the input is a zero-mean, wide sense stationary process with corre