Probability & Statistics v5 - Discrete random variables

Discrete random variables

A variable that takes only non-decimal numbers

Probability distributions for random variables

- In probability distributions for all random variables, the probabilities of each of the possibilities has to sum to 1, or 100%.

- The fact that a valid probability distribution always sums to 100 % allows us to find missing values in our data.

Expected value

Once we have a probability distribution for a discrete random variable, X, we can calculate the expected value E(X), which is the mean of X. The way we handle that with a discrete variable is by “weighting” each value.

Variance of discrete random variables

Standard deviation

We can also find the standard deviation of X, σX, which is just the square root of the variance of discrete random variables

Linear combinations of random variables

Linear combinations of random variables let us know what happens when we combine two data sets, either by adding them or subtracting them

Combinations of normally distributed variables

When we combine variables that are both normally distributed, the combination will be normally distributed as well.

Permutations

A permutation is the number of ways you can arrange a set of things, and the order matters.

Combination

A combination is the number of ways you can arrange a set of things, but the order doesn’t matter.