Do exponentially distributed random numbers have the memoryless property? Here is one way to find out. Generate many exponentially distributed random numbers with mean 3, using the formula in the...

Do exponentially distributed random numbers have the memoryless property? Here is one way to find out. Generate many exponentially distributed random numbers with mean 3, using the formula in the previous problem. Find the fraction of them that are greater than 1. This estimates the probability P(X
 1). Now find all random numbers that are greater than 4. Among these, find the fraction that are greater than 5. This estimates the probability P(X
 4
 1|X
 4). According to the memoryless property, these two estimates should be nearly equal. Are they? Try to do this without freezing the random numbers, so that you can get repeated estimates of the two probabilities by pressing the F9 key.