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set6 - ECSE-305 Winter 2009 Probability and Random Signals...

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ECSE-305, Winter 2009 Probability and Random Signals I Assignment #6 Posted: Tuesday, March 3, 2009. Due: Tuesday, March 10, 2009, 2h30pm (in class). Important notes: Assignments without this cover page will be discarded. Student #1: Name: ID: Student #2: Name: ID: Question Marks 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Total
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1. The PMF of a discrete RV X is given by p ( x ) = 1 / 15 , x ∈ { 1 , 2 , 3 , 4 , 5 } and p ( x ) = 0 otherwise. (a) Find E ( X ), E ( X 2 ) and V ar ( X ). (b) Let Y = X (6 X ). Find the PMF of Y , say p Y ( y ). (c) Find E ( Y ) using two different approaches 2. Suppose that on average, there is one typographical error in every 5 pages of a book. Assuming that the number of such errors on a single page is a Poisson random variable, what is probability of at leats one error on a specific page of the book. 3. Let X be a random number from [0 , 1]. Find the probability mass function of Y = nX , the greatest integer less than or equal to nX . 4. A right triangle has a hypotenuse of length 9. If the PDF of one side’s length is given by f ( x ) = braceleftbigg x/ 6 if 2 < x < 4 0 otherwise what is the expected value of the length of the other side?
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