Application for exponential distribution

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SUMMARY

The discussion centers on calculating the probability of an operation taking longer than 2 hours, given that the time follows an exponential distribution with a mean of 2 hours. The user correctly integrates the exponential probability function, yielding the cumulative distribution function as -e^{-y/2} + 1 for 0 ≤ y < ∞. The final calculation of 1 - P(Y≤2) results in e^{-1}, confirming the accuracy of the approach taken.

PREREQUISITES
  • Understanding of exponential distributions in probability theory
  • Knowledge of integration techniques for probability functions
  • Familiarity with cumulative distribution functions (CDF)
  • Basic skills in calculating probabilities using exponential functions
NEXT STEPS
  • Study the properties of exponential distributions in depth
  • Learn about cumulative distribution functions (CDF) and their applications
  • Explore integration techniques specific to probability functions
  • Practice calculating probabilities for different distributions, such as normal and Poisson
USEFUL FOR

Students and professionals in statistics, data science, and operations research who are interested in understanding and applying exponential distributions in real-world scenarios.

Askhwhelp
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The amount of time to finish a operation has an exponential distribution with mean 2 hours
Find the probability that the time to finish the operation is greater than 2 hours.

My thinking is to integrate the exponential probability function. After integrating it, I got -e^{-y/2} + 1 , 0 ≤ y < ∞

Then I use 1 - P(Y<=2) = 1 - (-e^{-2/2} +1) = e^-1

Is my approach correct? If so, could you check my answer please?
 
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Askhwhelp said:
The amount of time to finish a operation has an exponential distribution with mean 2 hours
Find the probability that the time to finish the operation is greater than 2 hours.

My thinking is to integrate the exponential probability function. After integrating it, I got -e^{-y/2} + 1 , 0 ≤ y < ∞

Then I use 1 - P(Y<=2) = 1 - (-e^{-2/2} +1) = e^-1

Is my approach correct? If so, could you check my answer please?

Yes, it is correct.
 

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