The time (in hours) required to repair a machine is an exponentially distributed random variable with parameter lambda = 1. What is the probability that a repair time exceeds 2 hours?

Zoie Frazier

Zoie Frazier

Open question

2022-08-18

The time (in hours) required to repair a machine is an exponentially distributed random variable with parameter λ=1.
What is the probability that a repair time exceeds 2 hours?

Answer & Explanation

etapi9a

etapi9a

Beginner2022-08-19Added 12 answers

Let X be exponential random variable that represents time required to repair a machine, X exp(1). We use what we know about exponential distribution.
P(X>x)=1F(x)=1(1eλx)=eλx
and for conditional probability:
P(X>t+s|X>t)=P(x>s)
P(X>2)=e2=0.135

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