Question

A random variable X is exponentially distributed with a mean of 0.20. a-1. What is the rate parameter λ? (Round your answer to 3 decimal places.) a-2. What is the standard deviation of X? (Round your answer to 2 decimal places.) b. Compute P(X > 0.32). (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.) c. Compute P(0.18 ≤ X ≤ 0.32). (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.)

Answer 1

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

λ = 1/mean = 1/0.2 = 5

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

sd = mean   in exponential distribution

hence sd = 5

b. Compute P(X > 0.32). (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.)

P(X > x) = e^(-lambda * x)

P(X > 0.32) = e^(-0.32 * 5) = 0.201896

= 0.2019

c. Compute P(0.18 ≤ X ≤ 0.32).

=e^(-5*0.18) - e^(-5 * 0.32)

= 0.20467

=0.2047

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