Question

14 There 2 dies. One is 8 sides (octahedral die) and another is 6 sides (normal). All are fair dies.
a. What is the expected value when the 2 dies tolled together
b. What is the variance when the 2 dies tolled together

Answer 1

First make a 6x8 table of the possible outcomes (sample space, 48 points).
For random throws, each of the 48 points has equal probability (p(i,j)=1/48).
a. Expected value of sum of two dice:
E[X]=Σ p(i,j)(i+j) i=1,8, j=1,6
Where p(i,j)=1/48, and i+j can be taken from the table.
b. variance
variance
=E[(X-E[X])^2
=E[X²]-E[X]&sup2
and
E[X²]=Σ p(i,j)(i+j)²

You are welcome to post your answer for a check.
Hint: E[X] and variance differ by 1/6.