i need help with this Suppose that the probability distribut

i need help with this

Suppose that the probability distribution of a random variable X is as shown below. Determine the mean and variance of the random variable Y = 3X.

Solution

mean of x=sum(x*p(x))

mean=4.5

v(x)=sum(x^2*p(x))-(mean)^2

sum9x^2*p((x))=25.5

V(x)=25.5-(4.5*4.5)=5.25

mean y=3x=3*mean(x)=3*4.5=13.5

V(Y)=3^2*V(X)=9*5.25=47.25

x	p(x)	x*p(x)
1	0.125	0.125
2	0.125	0.25
3	0.125	0.375
4	0.125	0.5
5	0.125	0.625
6	0.125	0.75
7	0.125	0.875
8	0.125	1
		4.5