# What is the mathematical formula for calculating the variance of a discrete random variable?

Let

By signing up, you agree to our Terms of Service and Privacy Policy

The mathematical formula for calculating the variance of a discrete random variable (X) is:

[Var(X) = \sum_{i=1}^{n} (x_i - \mu)^2 \cdot P(X = x_i)]

Where:

- (Var(X)) represents the variance of the random variable (X).
- (x_i) are the possible values of the random variable.
- (\mu) is the mean (expected value) of the random variable, given by (\mu = \sum_{i=1}^{n} x_i \cdot P(X = x_i)).
- (P(X = x_i)) is the probability mass function, representing the probability that the random variable takes the value (x_i).
- (n) is the total number of distinct values that the random variable can take.

This formula computes the average of the squared differences between each value of the random variable and its mean, weighted by the probabilities of those values occurring. It provides a measure of how spread out the values of the random variable are from its mean.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- What is a box plot and why are they used?
- What can covariance be used for?
- What is the variance of the data set 49, 2, 52, 15, 25, 9, 3, 5 to the nearest hundredth?
- How do you find the median on a cumulative frequency graph?
- There are three numbers with arithmetic mean 3 and two numbers with sum 26. Find the arithmetic mean of these five numbers. ?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7