Let X be an exponential random variable with a given parameter . Show (mathematically) that for any nonnegative t1, t2 the following expression is true:

P(Xt1) = P(X

(Hint: use the standard formulas for exponential distribution and conditional probability.)

This fact is often referred to as the "lack of memory" property of the exponential distribution. Give an example of a practical interpretation of this fact.