Suppose I roll n six-sided dice to get numbers X1 X2 . Consider the random variables: U = max{ X1 X2 . Xn } L = min{ X1 X2 .
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1.Suppose I roll n six-sided dice to get numbers X1 X2 ... Xn. Consider the random variables: U = max{ X1 X2 ...

Xn } L = min{ X1 X2 ... Xn } Write the cdf FU(a) and FL(a) for these variables, in terms of FX(a) HINT: the statement "max{ X1 X2 ... Xn } ≤ a" is the same as the statement that Xk ≤ a for every k. A similar statement can be made about min{ X1 X2 ... Xn. }.

HINT: the statement "max{ X1 X2 ... Xn } ≤ a" is the same as the statement that Xk ≤ a for every k. A similar statement can be made about min{ X1 X2 ... Xn. }.

2. For the previous problem (and exercise 4), write integrals for EU and EL, and compute the numerical value of EU and EL value when n=4.

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