3 In this question you will compute the variance of a geometric distribution with parameter p a Recall the following Taylor expansion 00 r 1 r r r and n 0 Use the fact that Taylor series can be differentiated term by term to show that 00 00 n 0 1 nr 1 1 2r 3r 1 r 1 r 1 n 2 2 n n 1 2 6r 12r 1 7 n 0 b Let X Geo p Express E X X 1 as an infinite series and use the previous result to show that E X X 1 2 2p p Var Y c Recall that E X and Var X E X E X Use these to show that 1 p