Question

Use Problemto $9$find the expected value of the sum of the numbers on the dice in Problem$2$.

Short answer

The expected value of the sum of the numbers on the dice is $E(x+y)=7$.

Step-by-step solution

Given Information

Two random variables defined over the same sample space.

Definition of the cumulative distribution function

The likelihood that a comparable continuous random variable has a value less than or equal to the function's argument is the value of the function

Prove the statement.

Two random variables defined over the same sample space.

x= number in first dice.

y= the number in second dice.

The average in first dice is given below.

$\begin{array}{c}{\mu }_x=E\left(x\right)\\ =\sum x_i{p}_i\\ =\frac{1}{6}\times (1+2+3+4+5+6)\\ =3.5\end{array}$

Both dice are equal hence average of first dice is same as average of second type.

$\begin{array}{c}E(x+y)=E\left(x\right)+E\left(y\right)\\ =3.5+3.5\\ =7\end{array}$

Hence, the expected value of the sum of the numbers on the dice is $E(x+y)=7$