P(50.6 < X < 51.8) =

Question

The lengths of a professor's classes has a continuous uniform distribution between 50.0 min and 52.0 min. If one such class is randomly selected, find the probability that the class length is between 50.6 and 51.8 min.

P(50.6 < X < 51.8) =

Answer 1

I propose five different methods, all connected, of course.

Method 1:

(51.8-50.6)/(52-50) = 1.2/2 = .6

Method 2.

If X ~ U[50, 52], f(x) = 1/(52-50) = 1/2 on [50,52]

Thus, P(50.6 <= X <= 51.8) = 1/2 (51.8 - 50.6) = 1/2(1.2) = .6

Method 3:

I[50.6, 51.8] 1/2 dx = 1/2 x E[50.6, 51.8] = 1/2 * 51.8 - 1/2 * 50.6 = .6

Method 4.

If X ~ U[50, 52], F(x) = 1/2x - 25 on [50, 52], so R[50.6 <= x <= 51.8] = F(51.8) - F(50.6) =

1/2 * 51.8 - (1/2 * 50.6 - 25) = .6

Method 5:

In R, for example, punif(51.8,min=50, max = 52) - punif(50.6,min=50, max = 52) = .9 - .3 = .6