# Expected Value and Variances

There are 2 fundamental quantities of probability distributions: expected value and variance.

Expected value:

• The simplest and most useful summary of the distribution of a random variable is the “average” of the values it takes on.
• (Please see references for equation)

Variance :

• The variance is a measure of how broadly distributed the r.v. tends to be.
• It’s defined as the expectation of the squared deviation from the mean:
• Var(X) = E[(X − E(X))2 ]
• In general terms, it is the expected squared distance of a value from the mean.

Looking at different distributions presents an interesting take on these two quantities:

1. Bernoulli Distribution
2. Uniform Distribution
3. Geometric Distribution
4. Binomial Distribution
5. Normal Distribution
6. Hypergeometric Distribution
7. Poisson Distribution

References:

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