4.1.5 Suppose that a symmetrical die is tossed n = 20 independent times. Work out the exact sampl...

Question

Question

4.1.5 Suppose that a symmetrical die is tossed n = 20 independent times. Work out the exact sampling distribution of the maximum of this sample.

Answer 1

Answer #1

Y = max(X1,x2,..X20)

P(Y<= y) = P(max(X1,x2,..X20) <= y)

= P(X1 < = y , X2 <= y,..X20 <= y)

=(P(X<= y))^20

=(y/6)^20

P(Y = y) = P(Y <= y) - P(Y <= (y-1))

=(y/6)^20 - ((y-1)/6)^20

Answer 2

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