試題詳解

十五. Consider the famous hat problemn. Suppose that n pcople throw their hats in a box and n each picks one hat at random. (Each hat can be picked by only one person, and cach assi of hats to persons is equally likely) Let X be a random variable that ropresents the number of people that get back their own hat. Which of the following statemnents is/are true?
(A) When n =3, P(X =3)=
(B) When n = 3, P(X = 1)=
(C) When n = 4, P(X = 3) = 0.
(D) When n = 4, E[X] = 2.
(E) When n = 5, E[X] = 1.