Question

A random variable X is exponentially distributed with an expected value of 52.

a-1. What is the rate parameter λ? (Round your answer to 3 decimal places.)

a-2. What is the standard deviation of X?

b. Compute P(44 ≤ X ≤ 60). (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.)

c. Compute P(41 ≤ X ≤ 63). (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.)

Answer 1

Let ,

The mean of exponential distribution of X is ,

The probability density function of X is ,

;

= 0 ; otherwise

a-1 ) The rate parameter

a-2 ) The standard deviation of X is ,

Standard deviation =

b.

c.