An old vending machine at the Greyhound Station sells Poptarts for $2.00 per package.The machine does not always dispense packages properly due to a faulty coiled release mechanism.Each time a customer operates the machine, it dispenses either zero, one, or two packages of Poptarts according to the following probability distribution:

x P(X = x)

0 p

1 1-2p

2 p

(a) Determine the expected value of X.

(b) Compute the variance of X (in terms of p).