Question

A random variable X is exponentially distributed with an expected value of 57.

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(54 ≤ X ≤ 60). (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.)

c. Compute P(45 ≤ X ≤ 69). (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.)

Answer 1

A random variable X is exponentially distributed with an expected value of 57

a-1)  What is the rate parameter λ?

Ans : parameter 1/57 = 0.0175

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

Ans : var = 1/57^2 = 0.000308

S.D. = sqrt(var) = 0.0175

b. ) Compute P(54 ≤ X ≤ 60).

Ans: P(54 ≤ X ≤ 60)=P(X ≤ 60).-P(X ≤ 54).

( using excel EXPODIST(X, PARAMETER,CUMULATIVE)

= 0.6501 - 0.6113

=0.0387

C. ) Compute P(45 ≤ X ≤ 69).

Ans: P(45 ≤ X ≤ 69)=P(X ≤ 69).-P(X ≤ 44).

( using excel EXPODIST(X, PARAMETER,CUMULATIVE)

= 0.7011 - 0.0.5450

=0.1560