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

 

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