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?

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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?

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Answer 1 · 2018-04-01T11:06:54

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 $\frac{6 \cdot 113}{113} = 6$ $(6 * 113)/113= 6$
Likewise,
The value of average in minimum would be $\frac{1 \cdot 113}{113} = 1$ $(1*113)/113 = 1$
Now,
Calculating average of maximum and minimum average can help us find where the values of actual average might be:
$\frac{7}{2} = 3.5$ $7/2 = 3.5$
Assuming that our average was 3.5,
Standard deviation = $\sum \sqrt[2]{\frac{x - ¯ x}{N - 1}}$ $sum root(2)( (x- bar x) / (N - 1))$
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): $\sum \sqrt[2]{\frac{(6 - 3.5) \cdot 113}{113 - 1}}$ $sum root(2)(( (6-3.5)*113) / (113 - 1))$

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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?

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