Question

Calculate the expected value of the sum of the two numbers obtained when two fair dice are rolled.

Answer 1

Sum of 2 Numbers

X = { 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 ,12 )

$p\left(x\right)=\left\{\frac{1}{36},\frac{2}{36},\frac{3}{36},\frac{4}{36},\frac{5}{36}\right\}$

$E\left(x\right)=\sum _{}^{}xi\left(p\right(x)=x)$

$=2\times \frac{1}{36}+3\times \frac{2}{36}+4\times \frac{3}{26}+5\times \frac{4}{36}+6\times \frac{5}{36}+7\times \frac{6}{36}+8\times \frac{5}{36}+9\times \frac{4}{36}+10\times \frac{3}{36}+11\times \frac{2}{36}+12\times \frac{1}{36}$

$\frac{2+6+12+20+30+42+40+36+30+22+12}{36}$

$\frac{252}{36}=7$