Costa Rica
Belinda Brown, belindabrownr04@gmail.com
- Probability Definitions: Introduction to probability definitions. Probability is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Maths to predict how likely events are to happen. The probability of an event can only be between 0 and 1 and can also be written as a percentage.
- Random Variables: Random variables present. A random variable is a mathematical formalization of a quantity or object which depends on random events. The term 'random variable' in its mathematical definition refers to neither randomness nor variability but instead is a mathematical function. Random variables are always real numbers as they are required to be measurable.
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Multiple Random Variables: Multiple random variables. Multiple random variables often come into play when we are interested in several variables that are related to each other. For example, in the experiment of tossing two fair dice, we might be interested in the sum of the two dice and the absolute difference of two dice. The joint probability mass functions (pmfs) of X and Y,
$$f_X(x) = P(X = x)$$ and$$f_Y(y) = P(Y = y)$$ , are given by$$f_X(x) = \sum_{y \in R} f_{X,Y}(x,y)$$ and$$f_Y(y) = \sum_{x \in R} f_{X,Y}(x,y)$$ - Random Processes: Random processes. A random or stochastic process is a random variable that evolves in time by some random mechanism. The variable can have a discrete set of values at a given time, or a continuum of values may be available. A random process (also called stochastic process) is an infinite collection of random variables, one for each value of time.
- Markov Chains: Markov chains. A Markov chain or Markov process is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. The defining characteristic of a Markov chain is that no matter how the process arrived at its present state, the possible future states are fixed.
- Probabilities & Statistical Scripts: This repository contains a collection of Python scripts related to probability and statistics