Grinstead-Snell-Probability · Problem 7.1.7

Sums of Random Variables

Mathematics · sums-discrete-random-variables-convolution

Problem

(a) A die is rolled three times with outcomes X1X_1, X2X_2, and X3X_3. Let Y3Y_3 be the maximum of the values obtained. Show that P(Y3≤j)=P(X1≤j)3 .P(Y_3 \leq j) = P(X_1 \leq j)^3\,. Use this to find the distribution of Y3Y_3. Does Y3Y_3 have a bell-shaped distribution? (b) Now let YnY_n be the maximum value when nn dice are rolled. Find the distribution of YnY_n. Is this distribution bell-shaped for large values of nn?

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