Question

Assume that X has an exponential distribution with parameter θ = 3.

A) Find P(X ≤ 1). Give your answer to 4 decimal places

B) Find P(2 ≤ X ≤ 10). Give your answer to 4 decimal places.

Answer 1

(A)
Probability Density Function of X is given by:

,

                     for x 0

         = 0,       for x <0

between limits 0 to 1.

Applying limits, we get:

So,

Answer is:

0.9502

(B)

between limits 2 to 10.

Applying limits, we get:

So,

Answer is:

0.0025