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Files HW 3 Х [ Homework 3 (1).pdf xD examples-joint-pdfs-soldvi × + File file:/i/CUsers/Clayt 203%20( 1 ).pdf 1. Consider a computer that has two operating systems installed on it. Let X and Y denote the number of timcs the computer freczes in a day when it runs on the tirst and the sccond operating systems, respectively Prix.y) 0.05 0.07 0.12 0.01 0.01 0.5 0.08 a. Find the marginal pmfs of X and Y b. Are X and Y independent? Justify your answer. c. Find ECX) d. Let Z-XY,which is the product of X and Y. Find the probability mass function of Z 2· Let X and Y be continuous random variables with joint pdf fLY (x, y)-3x. 0 and zero otherwise. y x 1. a. What is the marginal pdf of X? b. What is the marginal pdf of Y? c. What is the expectation of X alone? d. What is the covariance of X and Y? c. What is the corelation of X and Y? 3. Complete the following problems from the textbook Chapter 2: Problems 16,33,43.48 O Type here to search 8:03 PM 1/30/201

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solution (2)a) Moginal pdf of x 上(x) =3 2. 212 2 (2 3 (cJ 2을厂16-5 Su & O

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