HW6_solutions_b

HW6_solutions_b - HW#6, Solutions AMS 311 Probability...

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Unformatted text preview: 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); Lets calculate P(X=x, Y=y), notice if xy, 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,y0. Homework is due at the beginning of class on its due date. You must be in class and on time to submit your homework. No homework will be accepted via email. No late homework will be accepted. Your lowest homework grade will be dropped before computing your average. HW#6, Solutions AMS 311 Probability Theory (Spring 2011) As shown in the graph, it is the area above the straight line Y=X/z with density function f(x,y)...
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HW6_solutions_b - HW#6, Solutions AMS 311 Probability...

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