Tech Notes

My notes on Statistics, Big Data, Cloud Computing, Cyber Security

Probability

Used for Understanding and Quantifying Randomness.

A probability provides a quantitative description of the likely occurrence of a particular event. Probability is conventionally expressed on a scale from 0 to 1; a rare event has a probability close to 0, a very common event has a probability close to 1.

It is a measure or estimation of likelihood of occurrence of an event

Probability deals with predicting the likelihood of future events, while statistics involves the analysis of the frequency of past events.

Probability is primarily a theoretical branch of mathematics, which studies the consequences of mathematical definitions. Statistics is primarily an applied branch of mathematics, which tries to make sense of observations in the real world.

Outcome
An outcome is the result of an experiment or other situation involving uncertainty.

Event
An event is any collection of outcomes of an experiment.

Sample Space
The set of all possible outcomes of a probability experiment is called a sample space.

The probability of an event has been defined as

  • Its long-run relative frequency.
  • A personal degree of belief that a particular event will occur (subjective probability).

Independent Events
Two events are independent if the events have no influence on each other.

Mutually Exclusive Events (disjoint)
Two events are mutually exclusive (or disjoint) if it is impossible for them to occur together.

Conditional Probability
In many situations, once more information becomes available, we are able to revise our estimates for the probability of further outcomes or events happening. For example, suppose you go out for lunch at the same place and time every Friday and you are served lunch within 15 minutes with probability 0.9. However, given that you notice that the restaurant is exceptionally busy, the probability of being served lunch within 15 minutes may reduce to 0.7.

Addition Rule
The addition rule is a result used to determine the probability that event A or event B occurs, or both occur.

For Independent Events
Result ( probability that event A or event B occurs) => P(A)+P(B)-P(A).P(B)

For Disjoint Events
Result ( probability that event A or event B occurs) => P(A) + P(B)

Multiplication Rule
The multiplication rule is a result used to determine the probability that two events, A and B, both occur

Result (probability that event A and event B occur) => P(B|A).P(A) where
P(B | A) = the conditional probability that event B occurs given that event A has occurred already

Disclaimer : These are my study notes – online – instead of on paper so that others can benefit. In the process I’ve have used some pictures / content from other original authors. All sources / original content publishers are listed below and they deserve credit for their work. No copyright violation intended.

References for these notes :

The study material for the MOOC “Making sense of data” at Coursera.org
The study material for the MOOC “BerkeleyX: Stat2.2x Introduction to Statistics: Probability” at courses.edx.org

http://www.stats.gla.ac.uk/steps/glossary/probability.html#

https://www.cs.sunysb.edu/~skiena/jaialai/excerpts/node12.html

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