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# HW8 - HW#8 Due 05/04 Read Ross Chapter 7 Section 7.2 7.4...

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HW#8, Due 05/04 AMS 311 Probability Theory (Spring 2011) Read: Ross, Chapter 7, Section 7.2, 7.4, 7.7. Part 1 (10 points): PRINT your name and StonyBrook ID ( Last, First, #ID ) on the top on your work sheet. Staple your HW if more than 1 pages. Part 2: Problems (90 points) Write down your work step by step to get full score. You do not need to evaluate arithmetic expressions or integrals, if they are fully specified. For example, you may leave in this form. (1) (24 points) (a) If E(3X) = var(X/2) and var(2X) = 3, find (i) E[(2 + X) 2 ] and (ii) var(4 + 3X). (b) Suppose that X and W are independent and that var(W) = 7, E((X − W)(X + W)) = 100, E(3W) = 30, E(X 3 ) = 60, and E(X +W) = 12. Compute (i) var(X) and (ii) cov(X 3 ,W 2 ).. (2). (13 points) Let X have probability density function Compute the moment generating function, M X (t) of X. (3). (20 points) Consider a random variable X whose cumulative distribution function is given by We are also told that P(X > 3.3) = 0.25. (a) Find q, and compute the moment generating function, MX(t) of X.

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