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?
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>2)=e^(-2)=0.135