Students in an electrical engineering laboratory measure current in a circuit using an ammeter. Due to several random factors, the measurement, X, follows the probability density function f (x) = 0.025 x +

b, 2 < x < 6.

(a) Show that b = 0.15.

(b) Find the probability the measurement of the current exceeds 3 amps.

(c) Find E(X).

(d) Find the probability that all three laboratory partners measure the current independently as less than 4 amps.