Question

# A random variable XX with distribution Exponential(λ)Exponential(λ) has the memory-less property, i.e., P(X>r+t|X>r)=P(X>t) for all r≥0...

A random variable XX with distribution Exponential(λ)Exponential(λ) has the memory-less property, i.e.,

 P(X>r+t|X>r)=P(X>t) for all r≥0 and t≥0.P(X>r+t|X>r)=P(X>t) for all r≥0 and t≥0.

A postal clerk spends with his or her customer has an exponential distribution with a mean of 3 min3 min. Suppose a customer has spent 2.5 min2.5 min with a postal clerk. What is the probability that he or she will spend at least an additional 2 min2 min with the postal clerk?

X: time spent by a postal clerk with customer.

given that ,

the pdf of the distribution is:-

the probability that he or she will spend at least an additional 2 min with the postal clerk be:-

[ using memory-less property]

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