1 / 14

Basic Probability Theory and Statistics

This presentation guide you through Basic Probability Theory and Statistics, those are Random Experiment, Sample Space, Random Variables, Probability, Conditional Probability, Variance, Probability Distribution, Joint Probability Distribution, Conditional Probability Distribution (CPD) and Factor.<br><br>For more topics stay tuned with Learnbay.

learnbay_datascience
Download Presentation

Basic Probability Theory and Statistics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Basic Probability Theory and Statistics Swipe

  2. Basic Probability Theory and Statistics These are some very fundamental terms/concepts related to probability and statistics that often come across any literature related to Machine Learning and AI. Random Experiment Sample Space Random Variables Probability Conditional Probability Variance Probability Distribution Joint Probability Distribution Conditional Probability Distribution (CPD) Factor

  3. Random Experiment A random experiment is a physical situation whose outcome cannot be predicted until it is observed.

  4. Sample Space A sample space, is a set of all possible outcomes of a random experiment.

  5. Random Variables A random variable, is a variable whose possible values are numerical outcomes of a random experiment. There are two types of random variables. Discrete Random Variable is one which may take on only a countable number of distinct values such as 0,1,2,3,4,…….. Discrete random variables are usually (but not necessarily) counts. Continuous Random Variable is one which takes an infinite number of possible values. Continuous random variables are usually measurements.

  6. Probability Probability is the measure of the likelihood that an event will occur in a Random Experiment. Probability is quantified as a number between 0 and 1, where, loosely speaking, 0 indicates impossibility and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur.

  7. Conditional Probability Conditional Probability is a measure of the probability of an event given that (by assumption, presumption, assertion or evidence) another event has already occurred. If the event of interest is A and the event B is known or assumed to have occurred, “the conditional probability of A given B”, is usually written as P(A|B).

  8. Variance The variance of a random variable X is a measure of how concentrated the distribution of a random variable X is around its mean.

  9. Probability Distribution Is a mathematical function that maps the all possible outcomes of an random experiment with it’s associated probability. It depends on the Random Variable X , whether it’s discrete or continues. Discrete Probability Distribution: The mathematical definition of a discrete probability function, p(x), is a function that satisfies the following properties. This is referred as Probability Mass Function. Continuous Probability Distribution: The mathematical definition of a continuous probability function, f(x), is a function that satisfies the following properties. This is referred as Probability Density Function.

  10. Joint Probability Distribution If X and Y are two random variables, the probability distribution that defines their simultaneous behaviour during outcomes of a random experiment is called a joint probability distribution.

  11. Conditional Probability Distribution (CPD) If Z is random variable who is dependent on other variables X and Y, then the distribution of P(Z|X,Y) is called CPD of Z w.r.t X and Y. It means for every possible combination of random variables X, Y we represent a probability distribution over Z. There are a number of operations that one can perform over any probability distribution to get interesting results. Some of the important operations are :- Conditioning/Reduction Marginalisation

  12. Conditioning/Reduction If we have a probability distribution of n random variables X1, X2 … Xn and we make an observation about k variables that they acquired certain values a1, a2, …, ak. It means we already know their assignment. Then the rows in the JD which are not consistent with the observation is simply can removed and that leave us with lesser number of rows. This operation is known as Reduction.

  13. Marginalisation This operation takes a probability distribution over a large set random variables and produces a probability distribution over a smaller subset of the variables. This operation is known as marginalising a subset of random variables. This operation is very useful when we have large set of random variables as features and we are interested in a smaller set of variables, and how it affects output.

  14. Topics for next Post R-programming Data security Business analytics Stay Tuned with

More Related