1. Let XExp() (exponential random variable with parameter >0 ) and Y Geom(p) (geometeric random variable with parameter p(0,1) ). Show that both X and Y satisfy the "memoryless" property for random variables, that is P(Z>sZ>t)=P(Z>st) That is, the probability that the random variable will take values greater than s given the information that it has already taken values great than t, is the same as the probability that the random variable takes values greater than st. That is, we only need to take into account what has happened from time t to time s (anything that happened before time t is irrelevant to the probability calculation above). Hint: You will need to calculate the cdfs of both X and Y. Note that: P(Z>sZ>t)=P(Z>t)P(Z>sandZ>t).