What is the expected (average) value of the cube of the roll of a die? We know t

Question

What is the expected (average) value of the cube of the roll of a die?

We know that the average value of the roll of a die is 3.5 (it takes values 1, 2, 3, 4, 5, and 6 with equal probability). So would the average of the cube of the roll of a die be equal to the cube of 3.5? We can find that out through simulation.

In Excel, roll a fair die ( "=trunc(rand()*6)+1" ), and find the cube of that value (i.e. if you roll 5, its cube is 125). Now copy this to a thousand rows. Find the average of the cube, over those thousand values.

Explanation / Answer

the expected (average) value of the cube of the roll of a die = 1/6 (1^3+2^3 .. 6^3)

= 1/6 *((6*7/2))^2

= 73.5

by using =trunc(rand()*6)+1 in 1000 rows

we find average value = 79.159

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