EE 278B
Statistical Signal Processing
October 29, 2011
Handout #9
Homework #4 Solutions
1. (10 points) Coloring and whitening.
a. We denote the eigenvalue and eigenvector matrices of as and U , respec
EE 278B
Statistical Signal Processing
Tuesday, October 11, 2011
Handout #3
Homework #1 Solutions
1. (10 points) Exponential Random Variable.
a. It is easy to see that the CDF of X Exp() is FX (x) = 1
Lecture Notes 7
Stationary Random Processes
Strict-Sense and Wide-Sense Stationarity
Autocorrelation Function of a Stationary Process
Power Spectral Density
Stationary Ergodic Random Processes
EE
EE 278B
Statistical Signal Processing
October 20, 2011
Handout #6
Homework #4
Due Thursday, October 27
1. Coloring and whitening. Let
210
= 1 2 1 .
012
a. Find the coloring and whitening matrices of
EE 278
Statistical Signal Processing
October 24, 2015
Handout #9
Homework #4 Solutions
1. (10 points) Coloring and whitening.
a. We denote the eigenvalue and eigenvector matrices of as and U, respecti
EE 278B
Statistical Signal Processing
October 18, 2011
Handout #5
Homework #2 Solutions
1. (5 points) First available teller. The tellers service times are exponentially distributed, hence
memoryless.
EE 278 Statistical Signal Processing Homework #8 Due: Wednesday, December 2
November 18, 2009 Handout #18
1. Discrete-time Wiener process. Let cfw_Zn : n 0 be a discrete-time white Gaussian noise proc
EE 278
Statistical Signal Processing
October 9, 2009
Handout #5
Homework #2 Solutions
1. The cdf of random variable X is given by
FX (x) =
1
3
2
+ 3 (x + 1)2
1 x 0
x < 1
0
a. Find the probabilities of
EE 278B
Statistical Signal Processing
October 13, 2011
Handout #4
Homework #3
Due Thursday, October 20
1. Estimation vs. detection. Signal X and noise Z are independent random variables, where
X=
+1 w
EE 278B
Statistical Signal Processing
October 25, 2011
Handout #7
Homework #3 Solutions
1. (15 points) Estimation vs. detection.
a. We can easily nd the piecewise constant density of Y
1 |y | 1
4
1
f
EE 278 Statistical Signal Processing Homework #7 Solutions
November 20, 2009 Handout #19
1. Convergence examples. Consider the following sequences of random variables dened on the probability space (,
EE 278 Statistical Signal Processing Homework #1 Solutions
October 2, 2009 Handout #3
1. Monty Hall. (Bonus) Gold is placed behind one of three curtains. A contestant chooses one of the curtains. Mont
EE 278 Statistical Signal Processing Homework #6 Due: Wednesday November 4
October 28, 2009 Handout #10
1. Gaussian random vector Suppose X N (, ) is a Gaussian random vector with 1 110 = 5 and = 1 4
EE 278B
Statistical Signal Processing
September 29, 2011
Handout #1
Homework #1
Due Thursday, October 6
You can either hand the assignment to me after class or drop it in the
Homework In box in the EE
EE 278B
Statistical Signal Processing
Thursday, November 17, 2011
Handout #16
Homework #7
Due Thursday, December 1
1. Autocorrelation functions. Find the autocorrelation functions of
a. the process X
EE 278B
Statistical Signal Processing
October 6, 2011
Handout #2
Homework #2
Due Thursday, October 13
1. First available teller. A bank has two tellers. The service times for tellers 1 and 2 are indep
EE 278B
Statistical Signal Processing
Thursday, November 10, 2011
Handout #14
Homework #6
Due Thursday, November 17
1. Vector CLT. The signal received over a wireless communication channel can be repr
EE 278 Statistical Signal Processing Homework #5 Solutions
October 30, 2009 Handout #12
1. Additive-noise channel with path gain. Consider the additive noise channel shown in the gure below, where X a
EE 278B
Statistical Signal Processing
Tuesday, December 6, 2011
Handout #19
Homework #7 Solutions
1. (20 points) Autocorrelation functions.
a. The mean function is
X (t) = E[At + B ] = E[A]t + E[B ] =
EE 278B
Statistical Signal Processing
Friday, November 25, 2011
Handout #17
Homework #6 Solutions
1. (10 points) Vector CLT. The key point to this problem is to realize that we are asked to nd
the dis
EE 278
Statistical Signal Processing
October 18, 2007
Handout #6
Homework #4
Due Thursday, October 25
1. Two envelopes. A fixed amount a is placed in one envelope and an amount 5a is placed in the
oth
EE 278
Statistical Signal Processing
November 3, 2007
Handout #11
Homework #5 Solutions
1. (10 points) Additive-noise channel with path gain. First we find the mean and variance of Y
2
and its covaria
EE 278
Statistical Signal Processing
Tuesday, November 20, 2007
Handout #17
Homework #6 Solutions
1. (40 points) Gaussian random vector
a. The marginal pdfs of a jointly Gaussian pdf are Gaussian. The
EE 278
Statistical Signal Processing
Thursday, November 15, 2007
Handout #17
Homework #7
Due Thursday, November 29
1. Vector CLT. The signal received over a wireless communication channel can be repre
EE 278
Statistical Signal Processing
October 4, 2007
Handout #2
Homework #2
Due Thursday, October 11
1. The cdf of random variable X is given by
(1 2
+ 3 (x + 1)2
3
FX (x) =
0
1 x 0
x < 1
a. Find the
EE 278
Statistical Signal Processing
October 25, 2007
Handout #8
Homework #5
Due Thursday, November 1
1. PSfrag
Additive-noise
channel with path gain. Consider the additive noise channel shown in the
EE 278
Statistical Signal Processing
October 11, 2007
Handout #4
Homework #3
Due Thursday, October 18
1. Family planning. Alice and Bob choose a number X at random from the set cfw_2, 3, 4 (so the
out
EE 278
Statistical Signal Processing
Thursday, November 8, 2007
Handout #14
Homework #6
Due Thursday, November 15
1. Gaussian random vector Suppose X N (, ) is a Gaussian random vector with
1 1 0
1
EE 278
Statistical Signal Processing
September 27, 2007
Handout #1
Homework #1
Due Thursday, October 4
You can either hand the assignment to me after class or drop it in the
Homework In box in the EE