Question

A red die and a blue die are thrown. Let S be a random variable that denotes the square of the difference between the two numbers on the dice. For example, if the red die comes up 2 and the blue die comes up 5, then E(x):______

Answer 1

E(x) = 5.83

Explanation:

There are 36 possible outcomes.

There is a 6 in 36 chance that the difference between the dice is zero (square is also zero):

{1,1} {2,2} {3,3} {4,4} {5,5} {6,6}

There is a 10 in 36 chance that the difference between the dice is one (square is also 1):

{1,2} {2,1} {2,3} {3,2} {3,4} {4,3} {4,5} {5,4} {5,6} {6,5}

There is a 8 in 36 chance that the difference between the dice is two (square is 4):

{1,3} {3,1} {2,4} {4,2} {3,5} {5,3} {4,6} {6,4}

There is a 6 in 36 chance that the difference between the dice is three (square is 9):

{1,4} {4,1} {2,5} {5,2} {3,6} {6,3}

There is a 4 in 36 chance that the difference between the dice is four (square is 16):

{1,5} {5,1} {2,6} {6,2}

There is a 2 in 36 chance that the difference between the dice is four (square is 25):

{1,6} {6,1}

Therefore, the expected value for X is:

`E(X) = (6)/(36)*0+(10)/(36)*1+(8)/(36)*4+(6)/(36)*9+(4)/(36)*16+(2)/(36)*25\\E(X) = 5.83`

The expected value is E(x) = 5.83