Cheat sheet - Lol PDF

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Summary

Lol...

Description

Events Basic properties of events

Permutation (order matters) Arrange n distinct objects Arrange r objects from a set of n objects

Permutation when not all objects are distinct

l co Permutation in circle

Combination is the selection of n distinct objects without regard for order

Counting method Multiplication method

Addition principle

Discrete random variable Probability mass function (p.m.f)

Continuous random variable Cumulative distribution function (c.d.f)

Chebyshev's inequality

Cumulative distribution function (c.d.f)

Continuous mean

Two-dimensional random variable

Continuous variance Joint possibility density function for discrete RV

Marginal probability for discrete Discrete rv mean Mean and variance Discrete rv variance

Continuous random variable Probability density function (p.d.f) Joint probability function for continuous rv

Two-dimensional random variable

Binomial distribution

Conditional probability

Discrete distribution Discrete uniform distribution

Mean and variance

Independent random variable Condition for a binomial experiment It consist of n repeated Bernoulli trials Only two possible outcomes: success and failure in each trial

Mean/ expected value

P(Success)= p is the same constant in each trial Trials are independent

Mean and variance Negative binomial distribution

Bernoulli distribution

Poisson distribution Poisson approximation to binomial distribution

Discrete distribution Continuous uniform distribution

Binomial approximation to normal Large number law

Exponential distribution

Central limit theorem

Sampling and sampling distribution

Normal distribution

Random sampling

Standard normal

Sampling distribution of the difference of two sample mean

Chi-square distribution

T-distribution

Properties of t-distribution

Estimation based on normal distribution Sample variance

F-distribution

Estimation based on normal distribution Confidence interval for I mean Known variance and population normal or larger than 30

Unknown variance and population normal or close to normal small sample size

Unknown variance, population normal, n Confidence interval for difference btw 2 means

For paired data (dependent since 2 means are obtained from same sources

CI for a variance ( of normal population )

CI for ratio of 2 variance (normal) with a unknown means

Hypothesis testing...