Problem 76E

Let the random variable X have a discrete uniform distribution on the integers 0 ≤◊x ◊≤◊99. Determine the mean and variance of X.

Solution 76E

Step1 of 3:

Let us consider a random variable X, it follows discrete Uniform distribution with

X = [0,1,2,...,99].

We need to determine the mean and variance of X.

Step2 of 3:

Suppose that a random variable X follows discrete Uniform distribution with parameters [a, b]. Then, the probability mass function of Uniform distribution is given by:

x = 0,1,2,...,n.

We know that mean of Uniform distribution, and it is given by:

Therefore, Mean of X is 49.5.

Step2 of 3:

We know that Variance of Uniform distribution, and it is given by:

Therefore, Variance of X is 833.25.