tossing a fair die is an experiment that can result in any integer number from 1 to 6 with equal probabilities .let X be the number of dots face of a die .compute E(x) and var(x)

Question

kira_yamato · Answer

E(x) = 1(1/6) + 2(1/6) + 3(1/6) + 4(1/6) + 5(1/6) + 6(1/6) = 3.5
var(x) = [(1^2)/6 + (2^2)/6 + (3^2)/6 + (4^2)/6 + (5^2)/6 + (6^2)/6] - 3.5^2 = 2 11/12

anonymous · Answer

$$\Large  E(x)=1\cdot \frac16 +2\cdot \frac16+3\cdot \frac16+4\cdot \frac16+5\cdot \frac16+6\cdot \frac16=3.5$$

$$\Large \text{var}(x)=\frac{1^2}{6}+\frac{2^2}{6}+\frac{3^2}{6}+\frac{4^2}{6}+\frac{5^2}{6}+\frac{6^2}{6}-3.5^2=2\frac{11}{12}$$

@Kira_Yamato is this what you typed? ... just tell me if there's a multiply in $$2\frac{11}{12}$$ or not ... ;)     (THIS IS WHAT KIRA_YAMATO WROTE, I JUST REWROTE IT BETTER TOUNDERSTAND ;) )

anonymous · Answer

??

anonymous · Answer

$$find the \sum \to infinity 1+2x/1!+3x 2/2!+4x3/3!+...........+$$