Question

Let R as the space of all N! permutations of (1,2,...N). Which of the following statements is true?

a) P(Ri=k) = 1/N; for 1<=i, k<=N.
b) P(Ri=k, Rj=h) = 1/N(N-1); for 1<= i ≠j, k≠h<=N.
c) P(Ri=k, Rj=k) = 0; for 1<=i ≠j, k<=N.
d) All of the above.

Answer 1

The correct statement is b) P(Ri=k, Rj=h) = 1/N(N-1); for 1<= i ≠j, k≠h<=N.

Step-by-step explanation:

The correct statement is b) P(Ri=k, Rj=h) = 1/N(N-1); for 1≤ i ≠j, k≠h≤N.

To understand why this statement is true, we need to consider the permutations of (1,2,...N). Each permutation is equally likely, so the probability of Ri=k is 1/N for each i and k. The same reasoning applies to the probability of Rj=h. Since i and j are independent, the probability of both statements being true is the product of their individual probabilities, which is 1/N(N-1).

Therefore, statement b) is the correct answer.