CS1 April 2019, Q1 The amount of money customers spend in a single trip to the supermarket is modelled using an exponential distribution with mean €15. (i) Calculate the probability that a randomly selected customer spends more than €20. Probability = P(X>20) = 1-F(20) = exp(-4/3) (ii) Calculate the probability that a randomly selected customer spends more than €20, given that it is known that she spends more than €15. So we want P(X>20 | PX>15) - In the solution, this is worked out using bayes theorem i.e. P(X>20) /P(X>15). However, I thought as exponential distribution has a memoryless property, P(X>20 | X>15) = P(X>20)
Yes the exponential distribution does have the memoryless property, P(X>x+t|X>x)=P(X>t) so here that would be P(X>5)
