1. [-/2.64 Points] DETAILS MY NOTES DEVORESTAT9 4.1.001. The current in a certain circuit as measured by an ammeter is a continuous random variable X with the following density function. f(x) (0.025x + 0.4 3 x 5 otherwise ={0.025x+ (a) Graph the pdf. f(x) 0.6 0.5 0.4 0.3 0.2 0.1 x 1 2 3 4 5 f(x) 0.6 0.5 0.4 F 0.3 0.2 0.1 Verify that the total area under the density curve is indeed 1. L 5 0.025x + 0.4 dx = 3 = 2.3125 - (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). 1 2 3 4 5 f(x) f(x) 0.6 0.6 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 x 1 2 3 4 5 ASK YOUR TEACHER 1 2 3 4 5