Question

You get a standard six-sided die and where the one normally is you add some pips (dots on dice) to make the one into a five. So now this die has no one but two fives.

What is the variance of the number of pips showing on the die?

Answer 1

from above below is distribution of pips"

P(X=2) =P(X=3)=P(X=4)=P(X=6)=1/6

and P(X=5)=2/6

E(X) =xP(x)=2*1/6+3*1/6+4*1/6+6*1/6+5*2/6=25/6

E(X²)=x²P(x)=2^2*1/6+3^2*1/6+4^2*1/6+6^2*1/6+5^2*2/6=115/6

Variance =E(X²)-(E(X))² =115/6-(25/6)² =65/36