HW#6, Solutions
AMS 311 Probability Theory (Spring
2011)
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)
A table containing all possible (X,Y) values is listed below:
(6, 6);
(6, 5); (5, 5);
(6, 4); (5, 4); (4, 4);
(6, 3); (5, 3); (4, 3); (3, 3);
(6, 2); (5, 2); (4, 2); (3, 2); (2, 2);
(6, 1); (5, 1); (4, 1); (3, 1); (2, 1); (1, 1);
Let’s calculate P(X=x, Y=y), notice if x≠y, we have P(X=x, Y=y)=P((x,y) or
(y,x))=2*(1/6)*(1/6)=1/18. For example, P(X=4, Y=2)=P(first die gets 4, second die gets
2)+P(first die gets 2, second die gets 4).
If x=y, P(X=x, Y=y)= (1/6)*(1/6)=1/36.
Hence, the pmf for (X,Y) could be written as
A general solution for this type of questions could be found in Ch6.6 Order Statistics.
(2). (15 points)
Based on the independency,
we know
for x,y≥0.
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HW#6, Solutions
AMS 311 Probability Theory (Spring
2011)
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 Spring '08
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 Probability, Probability theory, probability density function, lowest homework grade

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