Question

A random variable X is exponentially distributed with a mean of 0.25.

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

Rate parameter ?

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

Standard deviation X

b.	Compute P(X > 0.34). (Round intermediate calculations to 4 decimal places and final answer to 4 decimal places.)

P(X > 0.34)

c.	Compute P(0.18 ? X ? 0.34). (Round intermediate calculations to 4 decimal places and final answer to 4 decimal places.)

P(0.18 ? X ? 0.34)

Answer 1

(a-1)

Rate parameter = = 1/0.25 = 4

(a - 2)

Standard deviation of X = 4

(b)

The probability density function of X is given by:

                       0 < X <

between limits 0.34 to

Applying limits, we get:

P(X>0.34) = 0.2567

(c)

between limits 0.18 to 0.34.

Applying limits, we get:
P(0.18 < X < 0.34) = 0.2301