A very large shipment of parts contains percent defectives. Two parts are chosen at random from the shipment and checked. Let the random variable $X$ denote the number of defectives found. Find the probability function of $X$. Answer the following, rounding your answers to four decimal places where appropriate.

(a) Find $P(X=0)$

(b) Find $P(X=1)$

(c) Find $P(X=2)$

(d) Find the mean of $X$

(e) Find the variance of $X$