The mean (expected value) and variance of a discrete uniform random variable can be calculated using the following formulas:

Mean (μ):
The mean or expected value of a discrete uniform distribution is simply the average of the minimum and maximum values. In this case, since the values are x1, x2,...,xk, the mean would be the average of these values.

μ = (x1 + x2 + ... + xk) / k

Variance (σ^2):
The variance is a measure of how spread out the numbers in the data set are. For a discrete uniform distribution, the variance is calculated by subtracting each value from the mean, squaring the result, and then averaging these square differences.

σ^2 = [(x1-μ)^2 + (x2-μ)^2 + ... + (xk-μ)^2] / k

Remember that these formulas are specific to a discrete uniform distribution, where each outcome xi has an equal probability of 1/k.

Question

The mean (expected value) and variance of a discrete uniform random variable can be calculated using the following formulas:

Mean (μ):
The mean or expected value of a discrete uniform distribution is simply the average of the minimum and maximum values. In this case, since the values are x1, x2,...,xk, the mean would be the average of these values.

μ = (x1 + x2 + ... + xk) / k

Variance (σ^2):
The variance is a measure of how spread out the numbers in the data set are. For a discrete uniform distribution, the variance is calculated by subtracting each value from the mean, squaring the result, and then averaging these square differences.

σ^2 = [(x1-μ)^2 + (x2-μ)^2 + ... + (xk-μ)^2] / k

Remember that these formulas are specific to a discrete uniform distribution, where each outcome xi has an equal probability of 1/k.

Knowee AI · Accepted Answer

The mean (expected value) and variance of a discrete uniform random variable can be calculated using the following formulas:

Mean (μ):
The mean or expected value of a discrete uniform distribution is simply the average of the minimum and maximum values. In this case, since the values are x1, x2,...,xk, the mean would be the average of these values.

μ = (x1 + x2 + ... + xk) / k

Variance (σ^2):
The variance is a measure of how spread out the numbers in the data set are. For a discrete uniform distribution, the variance is calculated by subtracting each value from the mean, squaring the result, and then averaging these square differences.

σ^2 = [(x1-μ)^2 + (x2-μ)^2 + ... + (xk-μ)^2] / k

Remember that these formulas are specific to a discrete uniform distribution, where each outcome xi has an equal probability of 1/k.

A random variable X that assumes the values x1, x2,...,xk is called a discrete uniform random variable if its probability mass function is f(x) = 1 k for all of x1, x2,...,xk and 0 otherwise. Find the mean and variance of X

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