1 let ydenote the nth order statistic of a random sample

Question

1. Let Y,,denote the nth order statistic of a random sample of size n from a distribution of the continuous type. Find th smallest value of n for which Pr (eo.9 <>Y,,) > 0.75.

2. Let Y1 <>Y2 <>Y3 <>Y4 <>Y5 denote the order statistics of a random sample of size 5 from a distribution of the continuous type. Compute:

(a) Pr ( Y, ,o5 Y5).

(b) Pr ( Y, ,o.25 Y3).

(c) Pr ( Y4 ,o.so Ys).