Question

A coin tossed and a die is rolled. The outcome of the coin is recorded 1 when it show a head and 0 when it shows a tail. The random variable R gives the sum of the outcomes of the coin and the die. Compute the average value of the random variables.

Answer 1

The sample space $S$ is given below,

$S=\begin{Bmatrix} 2 & 1 \\ 3 & 2\\ 4&3\\ 5&4\\ 6&5\\ 7&6 \end{Bmatrix}$

The probability distribution is,

$x$  1 2 3 4 5 6 7

$p(x)$ ${1\over 12}$ ${2\over12}$ $2\over12$ $2\over12$ $2\over12$ $2\over12$ $1\over12$

The expected value is given as,

$E(x)=\sum xp(x)=(1\times {1\over12})+(2\times {2\over12})+(3\times {2\over12})+(4\times {2\over12})+(5\times {2\over12})+(6\times {2\over12})+(7\times {1\over12})=4$ Therefore, the average of the random variable is 4.