Suppose that a fair die is tossed. What is the expected number of spots on the

uppermost face of the die when it comes to rest? Will this number of spots
ever be seen when the die is tossed?

Expectation value =

(1/6)*(1+2+3+4+5+6) = 3.5

That number will never be thrown, of course.

To find the expected number of spots on the uppermost face of a fair die, we need to calculate the mean value. Since a fair die has 6 faces numbered from 1 to 6, each face has an equal probability of landing face up. Therefore, the expected value is given by:

E(X) = (1 + 2 + 3 + 4 + 5 + 6) / 6
= 21 / 6
= 3.5

So, the expected number of spots on the uppermost face of the die is 3.5.

However, it's important to note that the expected value is not necessarily an actual value that can be observed when the die is tossed. Since the numbers on a die are discrete (whole numbers), the expected value can be a fractional or non-integer value, which means it may not correspond to any specific face on the die.

In this case, the expected value of 3.5 suggests that when the die is tossed numerous times, the average of the uppermost face values will converge towards 3.5. However, in a single toss, you will only see whole number values on the die faces (1, 2, 3, 4, 5, or 6).