Answer to Question #234810 in Statistics and Probability for talie

Question #234810

The life of an electronic device is known to have the exponential distribution with parameter λ = 1 1000 . (i) What is the probability that the device lasts more than 1000 hours? [2 marks] (ii) What is the probability it will last less than 1200 hours? [2 marks] (iii) Find the mean and variance of the life of the electronic device. 


1
Expert's answer
2021-09-09T04:54:14-0400

"\\lambda" is given as 1 100, which is not clear whether it is 11,000 or 1,000. I will use 1,000.

"f(x) = \\lambda e^{-\\lambda x}, x>0"

"\\lambda=1000"


i. "P(x)>1000"

"P(x)<1000=\\int_{1000}^{\\infin}1000 e^{-1000 x}dx"

"=-e^{-1000x}|_{1000}^{\\infin}"

"=0-0=0"


ii "P(x)<1200"

"P(x)<1200=\\int_{0}^{1200}1000 e^{-1000 x}dx"

"=-e^{-1000x}|_{0}^{1200}"

="0--1=1"


iii Mean and variance

The mean and variance of an exponential distribution is "\\lambda" .

Thus the mean of the distribution is 1000 and variance is 1000.


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