1Let the random variable X of the discrete type have the pdf

(1)Let the random variable X of the discrete type have the pdf given by the Table Find the expected value of 2x^2 + 5x +2 and the variance of 3X.

Solution

E(2x²+5x+2) = 2(6.7) +5(2.3) +2

                     = 13.4+11.5+2

                    = 26.9

Var(3x) = 9 var(X) = 12.69

					Total
x	1	2	3	4
p	0.4	0.1	0.3	0.2	1
xp	0.4	0.2	0.9	0.8	2.3
x^2p	0.4	0.4	2.7	3.2	6.7
Mean	2.3
Variance	1.41