Question

Assume a Poisson random variable has a mean of 8 successes over a 128-minute period.

a. Find the mean of the random variable, defined by the time between successes.

b. What is the rate parameter of the appropriate exponential distribution? (Round your answer to 2 decimal places.)

c. Find the probability that the time to success will be more than 55 minutes. (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.)

Answer 1

a.

Suppose that a Poisson random variable has a mean of 8 successes per 128-minute interval. Let X represent the time in seconds between successes. The random variable X follows an

exponential distribution with mean μ = 128 /8 = 16 minutes between successes.

b.

The distribution of X parameter λ = 1/ μ = 1/16 = 0.0625

c.

P(X >55) = 1 - P(X < 55)

P(X<=x) = 1 - e^-λx

P(X >55) = 1-(1 - e^-λ55) = e^-0.06255(55) = e^-3.44 = 0.0321

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