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Consider picking two numbers (X_1 and X_2) independently and equally likely between 1 and N.
(a) Determine the probability mass function for Y, the maximum of the two numbers.
(b) Determine the expected value (as a function of N) of the maximum (Y).
(c) Determine the probability mass function for the minimum W of the two numbers.
(d) Determine the expected value (as a function of N) of the minimum (W).
(e) As N → ∞ determine the ratio of the expected value of the maximum to N. That is, determine lim as N→∞ of E[Y]/N.
(f) As N → ∞ determine the ratio of the expected value of the minimum to N. That is, determine lim as N→∞ of E[W]/N.
Hint: Use Wolfram Alpha to solve summations needed in parts (b) and (d).
MUST INCLUDE WOLFRAM SCREENSHOT OF COMPUTATIONS
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