hw6 - ECE 302 Fall 2009 Division 2 Homework 6, due in class...

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ECE 302 Fall 2009 Division 2 Homework 6, due in class 10/15/2009 Problem 1. Let X and Y be independent random variables. Random variable X has a discrete uniform distribution over the set { 1 , 2 , 3 } , and Y has a discrete uniform distribution over the set { 1 , 3 } . Let V = X + Y , and W = X - Y . (a) Are V and W independent? Explain without calculations. (b) Find and plot p V ( v ). Also, determine E [ V ] and var( V ). (c) Find and show in a diagram p V,W ( v,w ). (d) Find E [ V | W > 0]. (e) Find the conditional variance of W given the event V = 4. (f) Find and plot the conditional PMF p X | V ( x | v ), for all values. Problem 2. An insurance company writes a policy to the e±ect that an amount of money x must be paid if some event A occurs within a year. If the company estimates that A will occur within a year with probability p , what should it charge the customer so that its expected pro²t will be 10% of x ? Problem 3
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