HW4_Spring11

HW4_Spring11 - ELEC210 Spring 2011 Homework-4 1. The random...

Info iconThis preview shows page 1. Sign up to view the full content.

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

Unformatted text preview: ELEC210 Spring 2011 Homework-4 1. The random variable X has cdf as shown in the figure below: (a) What type of random variable is X? (b) Find the following probabilities: , , , , , . 2. A point is selected at random inside a square defined by . Assume the point is equally likely to fall anywhere in the square. Let the random variable Z be given by the minimum of the two coordinates of the point. (a) Find the sample space S of the coordinates of the point and the sample space of Z, (b) Show the mapping from S to . . (c) Find the region in the square corresponding to the event . (d) Find the cdf of Z. (e) Use the cdf to find: . 3. A random variable X has pdf: (a) Find c. (b) Find (c) Find . . (d) Find the mean and variance of X. 4. A limiter is shown in figure below: (a) Find an expression for the mean and variance of for an arbitrary continuous random variable X. (b) Evaluate the mean and variance if X is a Laplacian random variable with . g(x) a -a x a -a 5. A binary transmission system transmits a signal X ( -1 to send a “0” bit; +1 to send a “1” bit). The received signal is Y=X+N where noise N has a zero-mean Gaussian distribution with variance . Assume that “0” bits are three times likely as “1” bits. (a) Find the conditional pdf of Y given the input value: and . (b) The receiver decides a “0” was transmitted if the observed value of y satisfies and it decides a “1” was transmitted otherwise. What is the probability that the receiver makes an error given that a “1” was transmitted? A “0” was transmitted? Assume . (c) What is the overall probability of error? 6. (a) Plot the pdf of a Gamma random variable for and λ with Matlab (Put the three curves in one figure). (b) Plot the pdf of a Laplacian random variable for curves in one figure). with Matlab (Put the three ...
View Full Document

Ask a homework question - tutors are online