Question

A random variable X is exponentially distributed with a mean of 0.23.

a) What is the standard deviation of X? (Round your answer to 2 decimal places.)

b) Compute P(X > 0.38). (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.)

c) Compute P(0.16 ≤ X ≤ 0.38). (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.)

Answer 1

Solution :

Given that ,

mean = 0.23

a)

The standard deviation of X = 1 / mean = 1 / 0.23 = 4.35

(b)

P(x > 0.38) = e^{-0.38 / 0.23} = 0.1916

(c)

P(0.16 ≤ X ≤ 0.38) = e ^-0.16/0.23 - e ^-0.38/0.23 = 0.3071