{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# ps8 - ECE 804 Random Signal Analysis Nov 23 2009 OSU Autumn...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ECE 804, Random Signal Analysis Nov. 23, 2009 OSU, Autumn 2009 Due: Dec. 2, 2009 Problem Set 8 Problem 1 Let the Gaussian random variable X ∼ N (0 , 1) and the Bernoulli random variable Z = ( 1 , with prob. 1/2- 1 , with prob. 1/2 be independent. Define Y = ZX . (a) Find f Y ( y ). (b) Show that X and Y are uncorrelated. (c) Find f Y | X ( y | x ) and f X,Y ( x,y ). (d) Are X and Y independent? Are they jointly Gaussian? Explain. Problem 2 Let X and Y be jointly uniform in the region enclosed by X > , Y > 0 and Y 6 2- 2 X . (a) Find f X ( x ) and f Y ( y ). (b) Find f Y ( y | X = x ). (c) If we observe that Y = 1, what is the expected value and the variance of X ? Problem 3 The random variable X is uniformly distributed in the interval between 0 and 1; the random variable Y is then selected from the interval between 0 and x with a pdf, f Y | X ( y | x ), that is symmetric about x/ 2. An example of a possible pdf is shown below....
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

ps8 - ECE 804 Random Signal Analysis Nov 23 2009 OSU Autumn...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online