Porisma

A hint to get started

Normalise the maximum score and count three-round orderings

An unbiased six-sided die is rolled twice. X is the higher value when they differ, or their common value when equal. Its distribution is P(X=r)=k(2r−1)P(X=r)=k(2r-1) for r=1,2,3,4,5,6.

(i) Find the exact value of k as a fraction in simplest form. marks

(ii) Find E(X)E(X). marks

One round consists of two rolls, with X as the score. A player plays three rounds.

(iii) Find the probability that the total score is 16. marks

[2017/TPJC/II/6]

CJC · Review problems · Question 2

The maximum has weights 1,3,5,7,9,11, rather than a uniform distribution.

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