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# HW6 - HW#6 Due 04/04 Read Ross Chapter 6 Sections 6.16.2...

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HW#6, Due 04/04 AMS 311 Probability Theory (Spring 2011) Read: Ross, Chapter 6, Sections 6.1–6.2. 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. (1). (10 points) Two fair dice are rolled. Find the joint probability mass function of X and Y , where X is the larger of the two values and and Y is the smaller of the two values on the dice. (e.g., if the roll is (4,2), then X = 4 and Y = 2, while if the roll is (4,4), then X = Y = 4) (2). (15 points) Let X and Y be independent exponential random variables with respective parameters 2 and 3. Find the cdf and density of Z = X/Y . Also, compute P(X < Y ). (3). (15 points) Suppose that X and Y have joint mass function as shown in the table below. (Here, X takes on possible values in the set {−2, 1, 3}, Y takes on values in the set {−2, 0, 1, 3.1}.) (a). (5 points) Compute P(X 2 > Y ).

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HW6 - HW#6 Due 04/04 Read Ross Chapter 6 Sections 6.16.2...

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