Probability and Statistics Problems and Solutions
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Are X and Y independent random variables?
Solution: First we calculate the marginal pdfs
Note that fX,Y (x, y) 6= fX(x) × fY (y). So they are not independent.
What is the conditional distribution of X, given Y = .50? What is the probability that less than 50% of the initiative 1 surveys are returned, given that 50% of the initiative 2 surveys are returned?
(c) Calculate E(X/Y = y). What is the expected proportion of initiative 1 surveys returned, given that 50% of the initiative 2 surveys are returned?
Three prisoners are informed by their jailer that one of them has been 1/3 1/2
First we label the prisoners as P1, P2 and P3. Suppose P1 asks the jailer to tell him privately whether P2 or P3 will be set free. Now we define the following events.
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