Calculating Probability for Exponential Distribution in Unplanned Shutdowns

In summary, the conversation is about finding the probability that the time between two unplanned shutdowns of a power plant is more than 21 days. The question is based on an exponential distribution with a mean of 20 days. The conversation includes a discussion on how to solve the equation and various calculations, with the final answer being 0.150. The person is asking for a review to confirm if their calculations are correct.
  • #1
Changoo
7
0
I am having a lot of trouble with a homework question from my book. It asks:

The time between unplanned shutdowns of a power plant has an exponential distribution with a mean of 20 days. Find the probability that the time between two unplanned shutdowns is more than 21 days.

I know this much so far 1-e-(20)(?) (one minus e to the negative power of mean times any value of the continuous variable(X))

I am lost on finding X within the equation.

Hope someone can help.
 
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  • #2
Hello!

First of all what do we define as an exponential distribution? It is equaled to:

1 - e^(-yx)

= 1 - e^(-20)(21)

Since this is the probability that the time between two unplanned shutdowns is less than 21 we don't need the 1. Hence our answer (I think) would be:

e^(-20)(21) or essentially 0.

Hope this helps!
 
Last edited:
  • #3
Thanks for your help,

But how do I solve E^-(20)(21)? I know that 20 times 21 is 420. How do I determine e^-420?

The book has given me some answers, but none say zero. a. .350, b. .650, c. .150, d. .850

I can probabily figure out the answer with no problem if someone can help me witht the problem above.
Thanks for your help!
 
  • #4
Okay, here is what I have, please tell me if I am right:

F(x)=1-e^-(20)(2/21)

F(x)=1-.850

F(x)=.150 (final answer)

I hope I am write.
 
  • #5
I meant right**** Sorry :blushing:
 
  • #6
Asking for Review

I feel confident about my answer, I am hoping someone can review and let me know if I have calculated wrong in any way. :approve:
 

What is the Exponential Distribution?

The Exponential Distribution is a probability distribution that describes the time between events that occur at a constant rate. It is often used to model the time between arrivals of customers at a store or the time between failures of a machine.

What are the key characteristics of the Exponential Distribution?

The Exponential Distribution has two key characteristics: a constant rate of occurrence and memorylessness. This means that the probability of an event occurring in a given time frame is independent of the time already elapsed.

What is the formula for the Exponential Distribution?

The probability density function (PDF) for the Exponential Distribution is given by f(x) = lambda * e-lambda * x, where lambda is the rate parameter and x is the time variable. The cumulative distribution function (CDF) is F(x) = 1 - e-lambda * x.

How is the Exponential Distribution related to other probability distributions?

The Exponential Distribution is closely related to the Poisson Distribution, which describes the number of events occurring in a given time interval. If the time interval is very small, the Poisson Distribution can be approximated by the Exponential Distribution.

What are some real-world applications of the Exponential Distribution?

The Exponential Distribution is commonly used in reliability engineering to model the time between failures of a system. It is also used in queuing theory to model the time between arrivals of customers at a store or the time between service requests at a call center. Other applications include finance, medicine, and environmental sciences.

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