The time (in hours) required to repair a machine is an exponentially distributed random variable with parameter lambda = 1. What is the conditional probability that a repair takes at least 3 hours, given that its duration exceeds 2 hours?

autumnunfound91

autumnunfound91

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2022-08-17

The time (in hours) required to repair a machine is an exponentially distributed random variable with parameter λ=1.
What is the conditional probability that a repair takes at least 3 hours, given that its duration exceeds 2 hours?

Answer & Explanation

Lina Watson

Lina Watson

Beginner2022-08-18Added 9 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>3X>2)=P(X>1+2X>2)=P(X>1)=e11=e1=0.368

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