Question

An octahedron was used as dice in a special edition of snakes and ladders. A player throws the die twice and takes the sum before making a move. Find the mean and variance of the sum of two throws of the die.

Answer 1

Octahedron has face numbered 1,2,3,4,5,6,7,8.

Table can be formed as,

Hence, the mean of the two throws of dice $= \dfrac{252}{28} = 9$

Also variance can be calculated using the formula :

$s = \dfrac{(3-9)^2+(4-9)^2+2(5-9)^2+2(6-9)^2+3(7-9)^2+3(8-9)^2+4(9-9)^2+3(10-9)^2+3(11-9)^2+2(12-9)^2+2(13-9)^2+(14-9)^2+(15-9)^2}{25} \\ Variance = \dfrac{36+25+32+18+12+3+12+18+32+25+36}{28}\\ Variance = 8.89$