Find the expected value and the standard deviation for the d

Find the expected value and the standard deviation for the discrete random variable:

y	0	1	2	3	4
Pr(Y = y)	0.3	0.17	0.17	0.3

P(Y=4)=1-0.3-0.17-0.17-0.3 = 0.06

expected value = E(Y) = sum of all y*f(y)

=0*0.3+1*0.17+2*0.17+3*0.3+4*0.06 = 1.65

E(Y^2) = sum of all y^2*f(y)

=0*0.3+1*0.17+2^2*0.17+3^2*0.3+4^2*0.06 =4.51

Variance= E(Y^2) - (E(Y))^2 = 4.51-1.65^2 =1.7875

So standard deviation =sqrt(1.7875) = 1.336974