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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 Spring '08
 Tucker,A
 Probability theory, probability density function, Randomness, Probability mass function

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