Probability Flashcards
Fixed event
An event where the outcome observed does not change i.e. death, the sun rising every morning etc.
Random event
an event where outcomes can vary: coin flip, football wins/losses, size of shits etc.
Probability
The likelihood that a certain outcome will occur
Bell-shaped (gaussian) distro
the theoretical symmetrical distro with the mean, median, and mode at the 50th percentile
Probability calculation
p(x)=f(x)/sample space
Sample space
The number of possible outcomes in a calculation of a probability
Standard Normal Distribution (Z distribution)
A symmetrical distro with a mean of 0 and an SD of 1
Standard Normal Transformation (Z transformation)
The method for changing a normal distribution with any mean and SD to the standard normal distro, with mean 0 and SD 1
Standard Normal Transformation Formula
z=x−μ/σ (population)
z=x−M/SD (sample)
“the given score, minus the mean divided by the standard deviation”
Z-score
The value on the x axis of a standard normal distro, specifically. It is the distance/number of Standard deviations above or below the mean, as a proportion. It is not the score, it is the difference relationship of the score to the standard deviation and the mean.
unit normal table
A numerical table that displays a list of z scores, their distance from the mean, and their distance from the tail, as ratios.
Mutually exclusive events
Events who’s outcomes are totally separate, not dependent on one another
Independent Outcomes
When the probability of an outcome does not affect the probability of another
Multiplicative Rule
p(A∩B)=P(A)*P(B)
Conditional Probability
Probability that is dependent on another condition being met beforehand
Conditional Probability Equation
p(A|B)=(A∩B)/P(A)
Bayes Theorem
Formula used to make inferences about parameters in a population
Bayes’ Theorem
p(A|B)=p(B|A)p(A)/p(B)
Random Variable
A variable in an experiment-describes the possible outcomes of an experiment
Probability distribution
Distribution of likelihoods from a random variable: sum of the probabilities equals 1.
Expected Value
The average outcome for a given random variable: the mean of the total outcomes
Expected Value formula
μ=Sigma (xp)
Multiply each possible outcome by the probability of its occurrence, and sum all of the products
Variance of a probability distro
The average squared variability of outcomes that deviate from the expected/average outcome
Variance of Probability formula
σ^2=Sigma (x−μ)^2*p
Standard Deviation of a probability distro
The average distance that expected random variable outcomes vary from the expected value.
Formula for Standard Deviation of Probability
sqrt σ^2=sqrt sigma (x-μ)^2*p
Binomial Probability Distro
Distro of probabilities for each outcome of a binary random variable (bivariate)
Bivariate Random Variable
Any random variable with two, and only two, random outcomes
Mean of a binomial distribution
The number of observations of the variable times the probability a given outcome will occur
Mean of a Binomial Distro formula
μ=np
Variance of a binomial distro
The squared variation of a binomial distribution with complementary outcomes
Variance of a binomial distribution formula
σ^2=np(1−p)
or
σ^2=npq (q=1-p)
Standard deviation of a binomial distro
The average variation between the two outcomes
Standard Deviation of a binomial distro formula
sqrt σ^2=sqrt npq (q=1-p)
