It is known that the shelf life of refills for a certain brand of purifier of water is exponentially distributed with an average of 3 years. Joe has already used his refill from said brand for 2 years in a row. What is the probability that Joe does not need change your water purifier refill in the next 2 years?

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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It is known that the shelf life of refills for a certain brand of purifier
of water is exponentially distributed with an average of 3 years. Joe has already used his refill from said brand for 2 years in a row. What is the probability that Joe does not need change your water purifier refill in the next 2 years?

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Step 1

Exponential Distribution: A continuous random variable X is said to follow Exponential distribution with parameter λ if its probability density function is given by,

Probability homework question answer, step 1, image 1

It is denoted by,

Probability homework question answer, step 1, image 2

The cumulative distribution function of X is given by,

Probability homework question answer, step 1, image 3

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