1. Let Yn denote the nth order statistic of a random sample of size n from a distribution of the continuous type. Find the smallest value of n for which the inequality P(ξ 0.9 n ) ≥ 0.75 is true. 2....

1. Let Yn denote the nth order statistic of a random sample of size n from a distribution of the continuous type. Find the smallest value of n for which the inequality P(ξ_0.9
n) ≥ 0.75 is true.

2. Let Y_1
2
3
4
5
denote the order statistics of a random sample of size 5 from a distribution of the continuous type. Compute:

(a) P(Y_1
0.5
5).

(b) P(Y_1
0.25
3).

(c) P(Y_4
0.80
5).