Probability Distributions - PMF vs PDF vs CDF vs More

There’s 2 many types of Probability distributions, including the PMF and PDF:

Notation:

X ~ Unif[a,b] → This is saying X is spread across a probability distribution according to the distribution Uniform.

PDF - Probability Density Function:

A probability distribution for continuous random variables.

PMF - Probability Mass Function:

A probability distribution for discrete random variables.

CDF - Cumulative Distribution Function:

At a point x, it gives the probability that the variable will take a value less than or equal to x. It’s non decreasing and can be thought of adding up all the probabilities until that point.

Calculating probability a variable falls between $x_1$ and $x_2$?

Simply do $P(x_2)-P(x_1)$.

Converting PDF to CDF

Integrate the PDF from $-\infty$ to the desired $x_1$. To go the other way, it’s the same process but deriving with respect to that variable.

Different Types:

There’s different types of distributions:

• Binomial Distribution
• Uniform Distribution
• Standard Normal Deviation