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Poisson and exponential distributions

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The maintenance department of a factory claims that the number of breakdowns of a particular machine follows a Poisson distribution with a mean of two breakdowns every 500hours. Let x denote the time (in hours) between successive breakdowns.

a. Find lambda and mu(x)

b. Write the formula for the exponential probability curve of x.

c. Sketch the probability curve.

d. Assuming that the maintenance department's claim is true, find the probability that the time between successive breakdowns is at most five hours.

e. Assuming that the maintenance department's claim is true, find the probability that the time between successive breakdowns is between 100 hours and 300 hours

f. Suppose that the machine breaks down five hours after its most recent breakdown. Based on the answer to part d, do you believe the maintenance departments claim?

Thank you for your help.

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This solution addresses the issues of number of breakdowns ...

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This solution addresses the issues of number of breakdowns over a specified time period and the time between breakdowns using Poisson and exponential probability distributuions

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