I got this question wrong on my midterm, can you please solve this and show steps/ work on how to figure this out? Thank you.

8. (5 points) The probability mass function (pmf) of random variable X is given below. Px(x) = p(1-p)l- where x=0 or x=1. (a) (2 points) Find the Moment Generating Function (MGF) of the pmf of random variable X (Hint: you only need to sum over . since x can only be either 0 or 1). 2 +x p " ( 1 - p ) V X=0 - 1. (0 0 ( 1 - p ) ) + tx (p]( 1 - p ) X Incorrect. -1.5 (b) (1.5 points) Use MGF to find E( X). E ( x ) = M etx p * ( 1 - p ) 2 - x P. (x ) Incorrect. -1.5 (c) (1.5 points) Use MGF to find V(X). V (x) = E(et x 2 ) - E (etx ) 2 Incorrect. -1.5