Consider two random variable X and Y

Question

Consider two random variable X and Y with following relation

Y = 2X+3

The probability distribution of X is given as follows:

X 3 4 6

p(X) 0.3 0.4 0.3

Find mean and variance of distributions X, Y.

Answer 1

mean of x = 3*0.3 + 4*0.4 + 6*0.3 = 0.43

x x^2 P(x) x^2*P(x)

3 9 0.3 2.7

4 16 0.4 6.4

6 36 0.3 10.8

19.9

var of x = 19.9 - (0.43)^2 = 19.72

E(Y) = E(2X + 3) = 2(EX) + 3 = 2(0.43) + 3 = 3.86

Var(Y) = Var(2x + 3) = Var(2x) = 4*Var(x) = 4*19.72 = 78.88