# What are the properties of expectation and variance?

## What are the properties of expectation and variance?

The expectation describes the average value and the variance describes the spread (amount of variability) around the expectation.

**What are the properties of expected values?**

Easy properties of expected values: If Pr(X ≥ a) = 1 then E(X) ≥ a. If Pr(X ≤ b) = 1 then E(X) ≤ b. Let Xi be 1 if the ith trial is a success and 0 if a failure.

### What is expected variation?

The expected value (or mean) of X, where X is a discrete random variable, is a weighted average of the possible values that X can take, each value being weighted according to the probability of that event occurring. The expected value of X is usually written as E(X) or m.

**Is variance always positive?**

Variance is always nonnegative, since it’s the expected value of a nonnegative random variable. Moreover, any random variable that really is random (not a constant) will have strictly positive variance.

## What is the value of the variance?

The variance (σ2) is a measure of how far each value in the data set is from the mean. Here is how it is defined: Subtract the mean from each value in the data. This gives you a measure of the distance of each value from the mean.

**What is the expected value and variance interpret your answer?**

The Expected Value of the random variable is a measure of the center of this distribution and the Variance is a measure of its spread.

### How do you find expected value and variance?

Variance: Var(X) To calculate the Variance: square each value and multiply by its probability. sum them up and we get Σx2p. then subtract the square of the Expected Value μ

**Can the variance of an expected value be negative?**

Can variance be negative? The answer: No, variance cannot be negative. The lowest value it can take on is zero. To find out why this is the case, we need to understand how variance is actually calculated.

## What is the use of variance in real life?

While risk and gambling get all of the credit in the real world, it’s the underlying variance that makes finance and gambling interesting. When you hear Jim Cramer yell that Tesla is too risky on Mad Money, you will know that means Tesla has a high degree of uncertainty; therefore, a high variance.