Hi! I am having problem doing this Markov's Inequality question, please please help.

Let X be some random variable with nite mean and variance which is not necessarily non- negative. The extended version of Markov's Inequality states that for a non-negative, monoton- ically increasing function (X) and a 0, Suppose lE[X] = 0, Var(X) = 02 0. (a) Use the extended version of Markov's Inequality stated above with (x) = (x + c)2, where c is some constant, to show that: 2 2P' ( X 2 a) S 0 + c (05 + c)2 (b) Note that the above bound applies for all positive c, so we can choose a value of c to minimize the expression, yielding the best possible bound. Find the value for c which will minimize the RHS expression (you may assume that the expression has a unique minimum). Plug in the minimizing value of c to prove the following bound: 2 IPXa