UCSD ECE153 Prof. Young-Han Kim
Handout #12 Thursday, April 14, 2011
Homework Set #3 Due: Thursday, April 21, 2011
1. Time until the n-th arrival. Let the random variable N(t) be the number of packets arriving during time (0, t]. Suppose N(t) is Poisson w

UCSD ECE153 Prof. Young-Han Kim
Handout #15 Thursday, April 21, 2011
Homework Set #4 Due: Thursday, April 28, 2010
1. Two independent uniform random variables. Let X and Y be independently and uniformly drawn from the interval [0, 1]. (a) Find the pdf of

UCSD ECE153 Prof. Young-Han Kim
Handout #18 Thursday, April 28, 2011
Homework Set #5 Due: Thursday, May 5, 2011
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 function g(y) that minimizes MSE =

UCSD ECE153 Prof. Young-Han Kim Homework Set #6 Due: Thursday, May 26, 2011
Handout #26 Thursday, May 19, 2011
1. Covariance matrices. Which of the following matrices can be a covariance matrix? Justify your answer either by constructing a random vector X

UCSD ECE153 Prof. Young-Han Kim Homework Set #7 Due: Thursday, June 2, 2011
Handout #33 Thursday, May 26, 2011
1. Symmetric random walk. Let Xn be a random walk defined by X0 = 0,
n
Xn =
i=1
Zi ,
1 where Z1 , Z2 , . . . are i.i.d. with Pcfw_Z1 = -1 = Pcfw

UCSD ECE153 Prof. Young-Han Kim
Handout #35 Thursday, May 26, 2011
Final Examination (Fall 2008)
1. Order statistics. Let X1 , X2 , X3 be independent and uniformly drawn from the interval [0, 1]. Let Y1 be the smallest of X1 , X2 , X3 , let Y2 be the medi

UCSD ECE153 Prof. Young-Han Kim
Handout #36 Thursday, May 26, 2011
Final Examination (Spring 2008)
1. Coin with random bias (20 points). You are given a coin but are not told what its bias (probability of heads) is. You are told instead that the bias is t

UCSD ECE153 Prof. Young-Han Kim
Handout #37 Thursday, May 26, 2011
Final Examination (Spring 2010) (Total: 180 points)
Your answer should be as clear, readable (and short) as possible.
1. Polya's urn revisited (40 points). Suppose we have an urn containin

UCSD ECE153 Prof. Young-Han Kim
Handout #19 Tuesday, May 3, 2011
Midterm Examination (Fall 2008) (Total: 120 points)
There are 3 problems, each problem with 4 parts, each part worth 10 points. Your answer should be as clear and readable as possible. In pa

UCSD ECE153 Prof. Young-Han Kim
Handout #20 Tuesday, May 3, 2011
Midterm Examination (Spring 2008) (Total: 80 points)
1. First available teller (20 points). Consider a bank with two tellers. The service times for the tellers are independent exponentially

UCSD ECE153 Prof. Young-Han Kim
Handout #21 Tuesday, May 3, 2011
Midterm Examination (Spring 2010) (Total: 120 points)
There are 3 problems, each problem with 4 parts, each part worth 10 points. Your answer should be as clear and readable as possible. 1.