Probability

Question 1

Fixed event

Answer 1

An event where the outcome observed does not change i.e. death, the sun rising every morning etc.

Question 2

Random event

Answer 2

an event where outcomes can vary: coin flip, football wins/losses, size of shits etc.

Question 3

Probability

Answer 3

The likelihood that a certain outcome will occur

Question 4

Bell-shaped (gaussian) distro

Answer 4

the theoretical symmetrical distro with the mean, median, and mode at the 50th percentile

Question 5

Probability calculation

Answer 5

p(x)=f(x)/sample space

Question 6

Sample space

Answer 6

The number of possible outcomes in a calculation of a probability

Question 7

Standard Normal Distribution (Z distribution)

Answer 7

A symmetrical distro with a mean of 0 and an SD of 1

Question 8

Standard Normal Transformation (Z transformation)

Answer 8

The method for changing a normal distribution with any mean and SD to the standard normal distro, with mean 0 and SD 1

Question 9

Standard Normal Transformation Formula

Answer 9

z=x−μ/σ (population)
z=x−M/SD (sample)
“the given score, minus the mean divided by the standard deviation”

Question 10

Z-score

Answer 10

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.

Question 11

unit normal table

Answer 11

A numerical table that displays a list of z scores, their distance from the mean, and their distance from the tail, as ratios.

Question 12

Mutually exclusive events

Answer 12

Events who’s outcomes are totally separate, not dependent on one another

Question 13

Independent Outcomes

Answer 13

When the probability of an outcome does not affect the probability of another

Question 14

Multiplicative Rule

Answer 14

p(A∩B)=P(A)*P(B)

Question 15

Conditional Probability

Answer 15

Probability that is dependent on another condition being met beforehand

Question 16

Conditional Probability Equation

Answer 16

p(A|B)=(A∩B)/P(A)

Question 17

Bayes Theorem

Answer 17

Formula used to make inferences about parameters in a population

Question 18

Bayes’ Theorem

Answer 18

p(A|B)=p(B|A)p(A)/p(B)

Question 19

Random Variable

Answer 19

A variable in an experiment-describes the possible outcomes of an experiment

Question 20

Probability distribution

Answer 20

Distribution of likelihoods from a random variable: sum of the probabilities equals 1.

Question 21

Expected Value

Answer 21

The average outcome for a given random variable: the mean of the total outcomes

Question 22

Expected Value formula

Answer 22

μ=Sigma (xp)

Multiply each possible outcome by the probability of its occurrence, and sum all of the products

Question 23

Variance of a probability distro

Answer 23

The average squared variability of outcomes that deviate from the expected/average outcome

Question 24

Variance of Probability formula

Answer 24

σ^2=Sigma (x−μ)^2*p

Question 25

Standard Deviation of a probability distro

Answer 25

The average distance that expected random variable outcomes vary from the expected value.

Question 26

Formula for Standard Deviation of Probability

Answer 26

sqrt σ^2=sqrt sigma (x-μ)^2*p

Question 27

Binomial Probability Distro

Answer 27

Distro of probabilities for each outcome of a binary random variable (bivariate)

Question 28

Bivariate Random Variable

Answer 28

Any random variable with two, and only two, random outcomes

Question 29

Mean of a binomial distribution

Answer 29

The number of observations of the variable times the probability a given outcome will occur

Question 30

Mean of a Binomial Distro formula

Answer 30

μ=np

Question 31

Variance of a binomial distro

Answer 31

The squared variation of a binomial distribution with complementary outcomes

Question 32

Variance of a binomial distribution formula

Answer 32

σ^2=np(1−p)
or
σ^2=npq (q=1-p)

Question 33

Standard deviation of a binomial distro

Answer 33

The average variation between the two outcomes

Question 34

Standard Deviation of a binomial distro formula

Answer 34

sqrt σ^2=sqrt npq (q=1-p)