Answer:
E(x) = 5.83
Step-by-step 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:
[tex]E(X) = \frac{6}{36}*0+\frac{10}{36}*1+\frac{8}{36}*4+\frac{6}{36}*9+\frac{4}{36}*16+\frac{2}{36}*25\\E(X) = 5.83[/tex]
The expected value is E(x) = 5.83
