You receive texts one at a time in your inbox. Let I'm be the time at which the nth text arrives (measured on a continuous scale from some starting point) Suppose that the waiting times between two texts are i.i.d. Exponential(1) Each text is non-spam with probability p, and spam with probability 1-p. (independent of the other texts and of the waiting times) Let X be the time at which the first non-spam text arrives. (i.e. X = T, if the first text is non-spam, X = 72 if the first text is a spam but the second isn't, etc) Find the mean E(X) b) Find the variance V(X) c) (Bonus) Find the MGF of X. What famous distribution does this follow? Show your result