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Sample Questions


Suppose there are 15 different color crayons in a box. Each time one obtains a crayon, it is equally likely to be any of the 15 types. Compute the expected # of different colors that are obtained in a set of 5 crayons. (Hint: use indicator variables and linearity of expectation)


We enumerate the crayons from 1 to 15. Let Xi indicate when the ith crayon 
is among the 5 crayons selected.

E(Xi) = Pr {Probability that at least one type i crayon is in set of 5}
E(Xi) = 1 – Pr {no type i crayons in set of 5}
E(Xi) = 1 – (145 /15)

Therefore, the expected # of crayons is:

= ∑15 E(Xi)
= 15[1-(145/15))]
= 4.38

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