A truncated discrete distribution is one in which a particular class cannot be observed and is eliminated from the sample space. In particular, if X has range 0, 1, 2, . . . and the 0 cannot be observed then the 0-truncated random variable XT has probability distribution function

P(Xt =x)= P(X =x)/P(X > 0) , x=1,2,3,...

Find the probability distribution functions, mean and variance of the 0-truncated random variable starting from X Pois().