What formula do you use to calculate the variance of a random variable?

What formula do you use to calculate the variance of a random variable?

• A. The expected value of the outcomes
• B. The sum of probabilities of events
• C. The expected value of the squared deviations from the mean
• D. The product of the mean and the distribution

Answer: (C)

To calculate the variance of a random variable, the correct approach is to focus on the expected value of the squared deviations from the mean. Variance measures the spread of a set of values around their mean, indicating how much the values deviate from that average. The formula for variance defined for a discrete random variable \(X\) is expressed as follows: \[ Var(X) = E[(X - \mu)^2] \] Where \(E\) denotes the expected value, and \(\mu\) is the mean (expected value) of \(X\). This formula essentially calculates how each possible outcome of the random variable deviates from the mean, squares that deviation to ensure all values are non-negative, and then finds the average of those squared deviations. In contrast, the other options presented do not accurately define variance. The expected value of outcomes refers to mean calculations, while the sum of probabilities of events relates to confirming that probabilities sum to one and does not represent variance. Lastly, the product of the mean and the distribution does not correctly capture the concept of variance since it oversimplifies the relationship between the outcomes and their spread. Hence, the focus on squared deviations from the mean solidifies the significance of the correct formula for

To calculate the variance of a random variable, the correct approach is to focus on the expected value of the squared deviations from the mean. Variance measures the spread of a set of values around their mean, indicating how much the values deviate from that average.

The formula for variance defined for a discrete random variable (X) is expressed as follows:

[

Var(X) = E[(X - \mu)^2]

]

Where (E) denotes the expected value, and (\mu) is the mean (expected value) of (X). This formula essentially calculates how each possible outcome of the random variable deviates from the mean, squares that deviation to ensure all values are non-negative, and then finds the average of those squared deviations.

In contrast, the other options presented do not accurately define variance. The expected value of outcomes refers to mean calculations, while the sum of probabilities of events relates to confirming that probabilities sum to one and does not represent variance. Lastly, the product of the mean and the distribution does not correctly capture the concept of variance since it oversimplifies the relationship between the outcomes and their spread. Hence, the focus on squared deviations from the mean solidifies the significance of the correct formula for