Question

A single six-sided die, whose faces are numbered 1 to 6, is rolled n times. The die is fair, each face is equally likely to land upward when the die is rolled. Let X be the number of times that the number on the upward face of the die is 1. Find the mean and the standard deviation of the random variable X.

Answer 1

Given a fair six sided die is rolled "n" times.

Let X be the number of times that the number on the upward face of the die is 1.

The probability of getting number 1 on upward face in any trial is p=1/6

Therefore,  

Hence the mean of X is



The standard deviation of X is