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?

1 Answers

Best Answer

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)=1-F(x)=1-(1-e^(- lambda x))=e^(- lambda x)

and for conditional probability:

P(X>t+s|X>t)=P(x>s)

P(X>3|X>2)=P(X>1+2|X>2)=P(X>1)=e^(-1*1)=e^(-1)=0.368

P(X>x)=1-F(x)=1-(1-e^(- lambda x))=e^(- lambda x)

and for conditional probability:

P(X>t+s|X>t)=P(x>s)

P(X>3|X>2)=P(X>1+2|X>2)=P(X>1)=e^(-1*1)=e^(-1)=0.368