Question

A fair die is rolled, and the result n is a number from {1; 2; 3; 4; 5; 6}. What is the average
value of n^2
2
?

Answer 1

91/6

Answer 2

Any idea how to do this using integration?

Answer 3

not sure how to this using integration, since the possible dice values are discrete.

Answer 4

i think you can just take the sum of the squares and then divide by 6

Answer 5

\[\int\limits_{-\infty}^{\infty} f(x) dx =1\]

Answer 6

the above must be true

Answer 7

not sure if this is the right way to answer this, but:
the probability of any one number is equal to 1/6.
this means that, the average of many times rolling the dice will be 3.5
3.5 squared is equal to 12.25
for example:
if you rolled the dice 600 times, then 100 times you will get 1, 100 times you will get 2, 100 times you will get 3, etc.
add them up and you get:
100*1 = 100
100*2 = 200
100*3 = 300
100*4 = 400
100*5 = 500
100*6 = 600
you get a sum total of number of 2100.
divide that by 600 and you get 3.5
square that and you get 12.25
this assumes i understood the problem correctly.