If a discrete random variable X has the following probability distribution: X -2, - 1, 0, 1, 2 P(X) 0.2, 0.3, 0.15, 0.2, 0.15 Use this to find the following: (a) The mean of X and E[X^2]. (b) The probability distribution for Y = 2X^2 + 2 (i.e, all values of Y and P(Y )). (c) Using part (b) (i.e, the probability distribution forY ), find E[Y ]. (d) Using part (a), verify your answer in part (c) for E[Y ].

If a discrete random variable X has the following probability distribution:

X      -2, - 1,     0,     1,      2

P(X) 0.2, 0.3, 0.15, 0.2,  0.15

Use this to find the following:

(a) The mean of X and E[X^2].

(b) The probability distribution for Y = 2X^2 + 2 (i.e, all values of Y and P(Y )).

(c) Using part (b) (i.e, the probability distribution forY ), find E[Y ].

(d) Using part (a), verify your answer in part (c) for E[Y ].

**Note: Please do not just copy from Chegg!