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HW4_Spring11

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

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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

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

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