Question

Market demand in the duration of 20 days follows normal distribution. The demand data for
20 days follow the series {100, 110, 120,…}. Consider the random variable X which takes the
values X=100, 110, 120,… Find the expectation of X and also variance of X

Answer 1

$E(X)=\sum XP(X)$

X follows an arithmetic series with $a=100$ and $d=10$

Sum of 20 terms is given by $10(200+(10×19))=3900$

$P(X)=\frac{1}{20}$

Thus, $E(X)=\frac{3900}{20}=195$

$Var(X)=E(X^2)-(E(X))^2$

$X^2$ Will be 10000, 12100, 14400...

Thus, $\sum X^2=827000$

$E(X^2)=\frac{82700}{20}=41350$

$Var(X)=41350-195^2=3325$