Question

Calculate the expected mean and expected standard deviation of the sample distribution of four 100-sided dice rolls.

Answer 1

We can relate the sample distribution of four 100-sided dice rolls to the event of rolling four 100-sided dice simultaneously and we assume the given dice are fair.

[ Here we want to use two famous formula for first n natural numbers.

#Sum of first n natural numbers= n*(n+1)/2

#Mean of first n natural numbers = (n+1)/2

#Variance of first n natural numbers = (n^2 - 1)/12 ]

We know that the expected value of rolling a '6-sided' die: (1+2+3+4+5+6)/6 = 3.5

The expected sum of rolling 4  '6-sided' dice: 4* (1+2+3+4+5+6)/6 = 14

Similarly, the expected value of rolling a '100-sided' die: (1+2+3+.......+100)/100 = 5050/100 = 50.5

The expected sum of rolling 4 '100-sided' dice: 4 * 50.5 = 202 (As the dice are fair)

The expected sum or Mean of the sample distribution of four 100-sided dice rolls: . (Ans.)

Now,

the expected variance of rolling a '100-sided' die: (100^2 -1)/12 = 833.25

The expected variance of rolling 4 '100-sided' dice: 4*833.25= 3333 (As the dice are fair)

The expected standard deviation of the sample distribution of four 100-sided dice rolls: (Ans.)

NOTE:

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