The current in a certain circuit as measured by an ammeter is a continuous random variable X with the following density function. f(x) = 0.075x + 0.2 3 ≤ x ≤ 5 0 otherwise
(a) Graph the pdf. WebAssign Plot WebAssign Plot WebAssign Plot WebAssign Plot Verify that the total area under the density curve is indeed 1. 5 0.075x + 0.2 dx 3 = 5 3 = 1.9375 − =

(b) Calculate P(X ≤ 4). How does this probability compare to P(X < 4)? P(X ≤ 4) < P(X < 4) P(X ≤ 4) > P(X < 4) P(X ≤ 4) = P(X < 4)

(c) Calculate P(3.5 ≤ X ≤ 4.5). Calculate P(4.5 < X).