Suppose the lifetime of a device T has an exponential distribution w.pdf
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The document addresses the calculation of the probability of a device's lifetime exceeding 4 given it lies between 2 and 5, assuming an exponential distribution with a mean of 3.5. It discusses the formula for the exponential distribution and provides an expression for finding specific probabilities. The final result of the calculation is approximately 0.3189.
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Suppose the lifetime of a device T has an exponential distribution w.pdf
- 1. Suppose the lifetime of a device T has an exponential distribution with parameter 3.5. Find the following probability: P(T > 4|2 < T < 5) Thanks! Solution exponential distribution f(x) =e^(-x) =1/mean =1/3.5 F(x) =1-e^(-x) now F(x>4) =F()-F(4) = (1-e^(-/3.5) )-(1-e^(-4/3.5)) =1-e^(-/3.5) -1+e^(-4/3.5) =1-0-1+0.31890 =0.3189 F(2