need this probability and statistic question, thank you with steps, thank

3. [10 points] The probability function fx for a random variable X is given by the table below. -1 0 2 3 fx (x) = P(X = x) 0.2 0.1 0.2 u (a) Find u. (b) Find the expected value and variance of the distribution for the random variable X: E(X) and Var(X). (c) Assume now Y = X - 2, then you may regard Y as another random variable. Find the expected value and variance for the distribution of this random variable Y: E(Y ) and Var(Y). (d) No need to answer this part. Just a remark for your interest: In part (c), you are finding E(X -2) and Var(X - 2). It would be interesting to compare these values with E(X) and Var(X)