Now let yn be the maximum value when n dice are rolled find, Basic Statistics

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Now let yn be the maximum value when n dice are rolled find

(a) A die is rolled three times with outcomes X1, X2, and X3. Let Y3 be the maximum of the values obtained. Show that

P (Y3 ≤ j) = P (X1 ≤ j)3 .

Use this to find the distribution of Y3. Does Y3 have a bell-shaped dis- tribution?

(b) Now let Yn be the maximum value when n dice are rolled. Find the distribution of Yn. Is this distribution bell-shaped for large values of n

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