Question

i. Consider a weighted 6-sided biased die that is twice as likely to produce any even outcome as any

odd outcome. What is the expected value of 1 roll of this die? What is the expected value of

the sum of 9 rolls of this die?

ii. Let X denote the value of the sum of 10 rolls of an unweighted 6-sided die. What is Pr(X =

0 mod 6)? (Hint: it is sufficient to consider just the last roll)

iii. What is the expected number of distinct faces that will be observed in m rolls of an n-sided

unweighted die? (Hint: dene indicator variable Xi which is 1 if the i'th face is never observed,

and use linearity of expectation). You may leave your answer as an expression in terms of m

and n.

Answer 1