Question

Calculate the expected value of x the sum of scores when two dice are rolled

Answer 1

Answer:

If we consider the possible outcomes from the throw of two dice: ... X as a random variable denoting the sum of the two dices, then we get ... So then we compute the expected value ...

Answer 2

Answer:

The expected value of x the sum of scores when two dice are rolled is 7.

Step-by-step explanation:

If we roll a die, there are total of six possible outcomes (1,2,3,4,5,6).

Sum of 2 Numbers

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

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

$\(\mathrm{E}(\mathrm{x})=\sum \mathrm{xi}(\mathrm{p}(\mathrm{x})=\mathrm{x})\)\\\(=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\) \(\frac{3}{36}+11 \times \frac{2}{36}+12 \times \frac{1}{36}\)$

$=\(\frac{2+6+12+20+30+42+40+36+30+22+12}{36}\)\\=\(\frac{252}{36}=7\)$

So, the expected value of x the sum of scores when two dice are rolled is 7.