For an “active” stock trader, the time between stock trades is exponentially distributed with a mean of 6 days. If active stock trader just traded some stock, what is the probability that it will be at least 7 days before another trade is made?

For the exponential distribution of n (the number of trades) the density function is f(x) = (1/6) exp(- x/6), x >= 0.

The probability P (n > 7) = integral^{+infty}_7 f(x) dx = exp( - 7/6) = 0.3114 ( 7 is the lower limit for the integral and +infinity is the upper limit).