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ps9 - ECSE-305 Winter 2009 Probability and Random Signals I...

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ECSE-305, Winter 2009 Probability and Random Signals I Assignment #9 Posted: Thursday, March 26, 2009. Due: Thursday, April 2, 2009, 2h30pm. 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. Let X be a Normal N (0 , σ 2 ) random variable, and let Y = X 2 . Are X and Y independent? Are they correlated? 2. Assume that the value of a resistor is a random variable R whose value in Ohm is uniformly distributed on (4 , 6). To this resistor, we apply a voltage V that is random and distributed according to a Normal N (10 , 1) density. Find the mean and the variance of the current flowing through the resistor. Assume that R is independent of V . 3. Let the joint probability mass function of random variables X , Y and Z be given by p ( x, y, z ) = braceleftbigg cxyz, if ( x, y, z ) ∈ R X × R Y × R Z 0 , otherwise where R X = { 4 , 5 } , R Y = { 1 , 2 , 3 } and R Z = { 1 , 2 } (a) Find the constant c? (b) Find the marginal PMF of the RVs X , Y and Z . (c) Find the joint marginal PMF of the pair X, Y , Y, Z and X, Z , i.e. find p XY ( x, y ), p Y Z ( y, z ) and p XZ ( x, z ).
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