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Let X be an exponential variable with unknown parameter . We know that P (X 10) = 5/9.
a. Find .
b. Compute P (X 15).
c. Compute P (X 15|X 10) (use the memoryless property).
d. Compute P (X 15|10 X 20).
e. (bonus) Find the number y > 0 for which P (y X 2y) is the largest.

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