Answer:
590.45
0.0825 mm^2
Step-by-step explanation:
Let us introduce the discrete uniform random variable Y with the parameters:
a = 0, b = 9
Calculate the mean and the variance:
E(Y)= 0 + 9/ 2 = 4.5
Var(Y)=(9-0+1)^2-1/12=8.25
Now observe that the random variable in the exercise - denoted X - is in fact:
X = 590 + Y/10
Now calculate:
E(X) = E (590.1 + Y/10) = 590.1 +E(Y)/10=590.45
Var(X) = E ((X — E(X))^2) = E ( (590 + Y/10-590 - E(Y)^2/10)
=E ((Y – E(Y))^2)/10
= Var(X)/100
= 0.0825 mm^2
