A fair six-sided die is rolled. What are E[X] and Var(X)?

How to answer

E[X]=(1+2+3+4+5+6)/6=3.5. E[X²]=(1+4+9+16+25+36)/6=91/6≈15.167. Var=E[X²]−(E[X])²=91/6−12.25=35/12≈2.917, so SD≈1.708. The mean 3.5 is also the classic 'what's a roll worth' answer.

Key idea: Mean is 3.5; use E[X²]=91/6, then subtract 12.25.