Question

The current in a certain circuit as measured by an ammeter is a continuous random variable X with the following probability density function:

f(x) = {kx +.2, 3<x<5

0 otherwise

a) what is the value of K

b) what is the mean of x

c) F_x(4) =

Answer 1

a) for this to be valid:

f(x) dx must be 1

f(x) dx = (kx+0.2) dx =(kx²/2+0.2x) |⁵₃ =8k+0.4 =1

k=0.6/8=0.075

b)

mean =E(X)= x f(x) dx = (0.075x²+0.2x) dx =(0.075x³/3+0.2x²/2) |⁵₃ =4.05

c)

F(4) = f(x) dx = (0.075x+0.2) dx =(0.075x²/2+0.2x) |⁴₃ =0.4625