Exponential Distribution (Chapter 14) M.I.G. McEachern High School.

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Presentation transcript:

Exponential Distribution (Chapter 14) M.I.G. McEachern High School

Exponential Distribution Exponential distributions are directly related to Poisson distributions If we have a discrete (a number we can count) number of events within a specific time, then there is a continuous (a number measured) time interval between the events. Exponential distributions calculate the probability of a certain time interval between events.

Exponential Distributions

Exponential Distributiond

Exponential Distribution Example 1: An electric motor's constant failure rate is failures/hr. Calculate the probability of failure for a 150 hr mission.

Example 1: If the electric motor's constant failure rate is failures/hr. Calculate probability of complete success for a 150 hr mission. Exponential Distribution

Example 1: An electric motor's constant failure rate is failures/hr. What is the Mean life expectancy E(x) = ? Exponential Distribution

Exponential Distribution Practice 1.If two customers arrive every 30 seconds on average, what is the probability of waiting less than or equal to 30 seconds for the next customer. What is the mean time between customers? 2.Accidents occur with a Poisson distribution at an average of 4 per week. Calculate the probability that at least two days will elapse between accidents? What is the mean time between accidents?

T.O.D. A CD player has an average record of successfully operating and providing listening enjoyment for more than 5,000 hours on the average before requiring repairs. A customer is planning on buying a CD player for installation in a boat that will be taking an extended cruise that will demand 4,000 hours of play before being able to obtain repairs or routine maintenance. How reliable will the CD player be for the customer? (Assume an exponential distribution)