Suppose X 1 , , X 1 00 are independent and uniformly distributed on (0, 1) (a) Find the probability the 25th smallest variable is less than 0 20 (b) Find E X (95) and V X ( 95) (c) The range of a set of numbers is the difference between the maximum and the minimum Find the expected range ...

a The 25th smallest variable is X 25 X 25 Be ...

Suppose X 1 , . . . , X 1 00 are independent and uniformly distributed on

Question:

Suppose X₁, . . . , X₁₀₀ are independent and uniformly distributed on (0, 1).
(a) Find the probability the 25th smallest variable is less than 0.20.
(b) Find E[X₍₉₅₎] and V[X₍₉₅₎].
(c) The range of a set of numbers is the difference between the maximum and the minimum. Find the expected range.