hw2 - EE 278 September 30, 2009 Statistical Signal...

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

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: EE 278 September 30, 2009 Statistical Signal Processing Handout #2 Homework #2 Due: Wednesday October 7 1. Probabilities from cdf. The cdf of random variable X is given by F X ( x ) = braceleftBigg 1 3 + 2 3 ( x + 1) 2- 1 x x <- 1 a. Find the probabilities of the following events. A = { X > 1 3 } , B = {| X | 1 } , C = {| X- 1 3 | < 1 } , D = { X < } . b. Does X have a pdf? Explain your answer. 2. Distance to nearest star. (Bonus) Let the random variable N be the number of stars in a region of space of volume V . Assume that N is a Poisson random variable with pmf p N ( n ) = e- V ( V ) n n ! , n = 0 , 1 , 2 ,..., where is the density of stars in space. We choose an arbitrary point in space and define the random variable X to be the distance from the chosen point to the nearest star. Find the pdf of X in terms . 3. Additive Gaussian noise channel. A communication channel has a real-valued input signal X and an output Y = X + 2 Z , where Z N (0 , . 09). Suppose that X =- 1 is sent. Use the attached table of the Q ( ) function to find the probability of the event { Y > } . 4. Lognormal pdf. Let X N (0 , 2 ). Find the pdf of Y = e X ....
View Full Document

This note was uploaded on 11/28/2009 for the course EE 278 taught by Professor Balajiprabhakar during the Fall '09 term at Stanford.

Page1 / 4

hw2 - EE 278 September 30, 2009 Statistical Signal...

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

View Full Document Right Arrow Icon
Ask a homework question - tutors are online