Question

A fair die is rolled n=113 times, each time observing the number of dots appearing on the topside of the die. The number of dots showing on the topside of toss i is a random variable represented by Xi. What is the mean and standard deviation of Xi?

Answer 1

As it's totally random and the answer can't be trusted upon,
The maximum number of dots in a die: 6
The least number of dots in a die: 1
Now,
The value of average in maximum would be `(6 * 113)/113= 6`
Likewise,
The value of average in minimum would be `(1*113)/113 = 1`
Now,
Calculating average of maximum and minimum average can help us find where the values of actual average might be:
`7/2 = 3.5`
Assuming that our average was 3.5,
Standard deviation = `sum root(2)( (x- bar x) / (N - 1))`
Assuming that mean is 3.5 and all the dots were 6(Mean can't be 3.5 when all the dots were 6 but still trying to just get an estimate),
S.D would be somewhere around (guess): `sum root(2)(( (6-3.5)*113) / (113 - 1))`