Estimate exponential distribution parameter

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SUMMARY

The discussion focuses on estimating the expected time of operation for a transistor with an exponentially distributed lifespan. After testing 400 transistors, it was determined that 109 transistors remained operational after one time unit. The estimation method involves approximating the situation with a Binomial distribution, where the probability of survival, p, is calculated as p* = 109/401, leading to the equation p = e^(-1/μ) for the exponential distribution. This relationship is crucial for understanding the survival probability in the context of exponential decay.

PREREQUISITES
  • Understanding of exponential distributions and their properties
  • Familiarity with Binomial distribution concepts
  • Knowledge of survival analysis in statistics
  • Basic proficiency in probability theory
NEXT STEPS
  • Study the derivation of the relationship between Binomial and Exponential distributions
  • Learn about survival functions in exponential distributions
  • Explore the method of maximum likelihood estimation for parameter estimation
  • Review practical applications of exponential distributions in reliability engineering
USEFUL FOR

This discussion is beneficial for students in statistics, engineers working with reliability analysis, and anyone involved in modeling lifetimes of products using exponential distributions.

Gauss M.D.
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Homework Statement



A certain type of transistor has an exponentially distributed time of operation. After testing 400 transistors, it is observed that after one time unit, only 109 transistors are working.

Estimate the expected time of operation.


Homework Equations





The Attempt at a Solution



It was suggested that I approximate with

X ≈ Bin(400,p)

Then conclude that p can be estimated with p* = 109/401 = e-1/μ

That part I don't get is: why is p = e-1/μ ?
 
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In an exponential distribution, what is the probability that something survives for a time t? Then set t=1.
 

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