EE 278 Statistical Signal Processing Homework #3 Due Monday, July 20, 2009 1. Schwarz inequality. a. Prove the following inequality: (E(XY )2 E(X 2 )E(Y 2 ) . Hint: Use the fact that E(X + aY )2 ) 0 for any real number a .
Monday, July 13, 2009 Handout #6
EE 278 Statistical Signal Processing Homework #5 Due Wednesday, August 12, 2009 1. Absolute value random walk. Let Xn be a random walk defined by
n
Monday, August 3, 2009 Handout #14
X0 = 0, Xn =
i=1
Zi ,
n 1,
where cfw_Zi is an i.i.d. process with P(Z1
EE 278
Statistical Signal Processing
Wednesday, August 12, 2009
Handout #15
Homework #5 Solutions
1. (10 points) Absolute value random walk.
a. This is a straightforward calculation and we can use results from lecture notes. If k 0
then
Pcfw_Yn = k = Pcf
EE 278
Statistical Signal Processing
Handout #13
Monday, August 3, 2009
Homework #4 Solutions
1. (10 points)
(a) The marginal pdfs of a jointly Gaussian pdf are Gaussian. Therefore X1
N (1, 1).
(b) Since X2 and X3 are independent (23 = 0), the variance o
EE 278 Statistical Signal Processing Homework #3 Solutions 1. (20 points) Schwarz inequality. a. Consider the quadratic equation in the parameter a :
Monday, July 27, 2009 Handout #7
0 = E(X + aY )2 ) = E(X 2 ) + 2aE(XY ) + a2 E(Y 2 ) . Since it is the ex
EE 278
Statistical Signal Processing
Handout #5
Monday, July 20, 2009
Homework #2 Solutions
1. (15 points) The general formula for calculating the pdf of a dierentiable function of
a continuous random variable given in the lecture notes is
fY (y ) =
k : f
EE 278 Statistical Signal Processing Homework #1 Solutions 1. (15 points)
Handout #4 Monday, July 13, 2009
(a) The sample space consists of triplets of the form (curtain with gold behind it, curtain chosen by player, curtain that Monty opens). If we denot
EE 278 Statistical Signal Processing Homework Set #4 Due: Monday, August 3, 2004.
Handout #12 Monday, July 27, 2009
1. Given a Gaussian random vector X N (, ), where = [ 1 5 2 ]T and 1 1 0 = 1 4 0 . 0 0 9 Find the pdfs of the following random variables. (
EE 278 Statistical Signal Processing Homework Set #2 Due: Monday, July 13, 2009.
Handout #3 Monday, July 6, 2009
1. Random phase signal Let Y (t) = sin(t + ) be a sinusoidal signal with random phase U [-, ] . Find the pdf of the random variable Y (t) for
EE 278 Statistical Signal Processing Homework Set #1 Due: Monday, July 6, 2004.
Handout #2 Monday, June 29, 2009
Announcement: The homework is due next Monday. You can either hand it in after class or deposit it, before 5pm, in the Homework in box in the