The pressure P, in lb ft−2, developed at the wings of an aircraft is given by P = 3 ⋅ 10−3V2, where V is the velocity (in miles per hour) of the wind surrounding the wings. The pressure can be considered as a random variable with density function f (p) = c

√

p

, 0 ≤ p ≤ a, for c > 0 and a > 0.

(i) Find the value of c if it is known that E(P) = 0.1 lb ft−2.

(ii) Find the distribution function and the expected value of the velocity V.