Suppose we roll two tetrahedral dice that have 0 0 10 20 on

Suppose we roll two tetrahedral dice that have 0, 0, 10, 20 on their four sides. Let Y be the sum of the two numbers. Find the expectation and the variance of Y.

Solution

The distubution function of Y is

P(score=x)=x-1/16

    P(X=0)=-1/16

   P(X=0)=-1/16

P(X=10)=9/16

P(X=0)=19/16

           E(Y) = xP(Y = y)

                   =0(-1/16)+0(-1/16)+10(9/16)+20(19/16)

                   =5.625+23.75

                   =29.375

   E(Y)=29.375

      Var(Y) = E(Y²) (E(Y))²    

E(Y²)   = 0²(-1/16)+0²(-1/16)+10²(9/16)+20²(19/16)

                     =56.25+475

                     =531.25

Var(Y)=531.25+(29.375)²

                        =531.25+862.890

                  =1394.140

     Var(Y)=1394.140