CAS MA 581: Probability
A2 Midterm 1
CAS MA 581代写 Three prisoners, A, B, and C, are on death row. The governor decides to pardon one of the three and chooses at random the prisoner to pardon.
Note: CAS MA 581代写
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1. CAS MA 581代写
Consider the following variation of the three prisoners problem:
Three prisoners, A, B, and C, are on death row. The governor decides to pardon one of the three and chooses at random the prisoner to pardon. He informs the warden of his choice but requests that the name be kept secret for a few days.
The next day, A tries to get the warden to tell him who had been pardoned. The warden refuses. A then asks which of B and C will be executed. The warden thinks for a while, then tells A that B is to be executed.
Suppose we know that if A were to be pardoned, the warden would tell A that B is to be executed with probability 1/3 or that C is to be executed with probability 2/3 .
(a) Calculate the probability that the warden tells A that B is to be executed.
(b) What is the probability that A is pardoned given that the warden tells A that B is to be executed?
(c) If A is then given the option to switch fates with C, should he do that? Why or why not?
2. CAS MA 581代写
Suppose X and Y are random variables with joint PMF
where r > 0 is some given positive parameter.
(a) Find the marginal PMF ᵖᵡ(x) as a function of c.
(b) Find the marginal PMF ᵖᵡ (y) as a function of c
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