X^2/30, for X = 1,2,3,4

Question

Find the variance and standard deviation of the probability distribution

X^2/30, for X = 1,2,3,4

Answer 1

(1/30+ 4/30+ 9/30+ 16/30)/4= mean = 1/4 = (7.5)/30

1/30 - 7.5/30 = -5.5/30

4/30 - mean = - 3.5/30

9/30 - mean = 1.5/30

16/30 - mean= 8.5/30

differences squared = 30.25/900

12.25/900

2.25/900

72.25/900

sum fo squares = 117/900

divide by 4 if it's a population

Variance = 117/3600

take the square root

sd = standard deviation = sqr(117)/3600 = sqr(117)/36 = about 0.3