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In each problem, make sure that you are clearly defining random variables, stating their distributions, and...

In each problem, make sure that you
are clearly defining random variables, stating their distributions, and writing down the formulas that you
are using. (That is, write down the pmf, write down mean and variance formulas.)

Prove that the exponential distribution is memoryless. That is, let X~Exp(?), and show that for any two positive real numbers x, y, P(X ≥ x + y | X ≥ y) = P(X ≥ x). Hint: Mirror the proof we did in class for the geometric distribution. Use the definition of conditional probability and simplify

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