Probability, Random Variables, and Probability Distributions

Consensus Gathering

Stratified Analysis

Sample Survey

Random Sampling

Voluntary response sample

Simple random sample (SRS)

Judgment sample

Quota sample

Circumference(circle)/Circumference(square)

Radius(circle)^2/Radius(square)^2

Diameter(square)/Diameter(circle)

Area(circle)/Area(square)

0.50

0.25

0.06

0.14

If $P(Spam|Keywords) > P(Spam)$, this implies that those keywords increase our belief that the message is spam.

These keywords have no effect on the probability of the message being spam, as missing such words are common in non-spam emails too.

These keywords ensure that the email will not be spam because they significantly decrease the probability of it being so.

Spamming emails are less likely to contain these keywords, thus reducing our assumption that a message is spam.

Calculating standard deviations separately for each population's predicted probabilities then comparing them directly.

Using a chi-square test for independence on frequencies of A and B occurring together in both populations.

Applying hypothesis testing to compare differences in predictive accuracies for $P(A|B)$ between two populations using bootstrapping techniques.

Implementing ANOVA to evaluate group differences based only on unconditional probabilities within each population.

0.7273

0.28

0.385

0.35

Event Y happens less frequently when event X occurs than at any other time.

Event X prevents event Y from happening more often than it would naturally occur on its own.

Knowing X occurred increases the likelihood of Y occurring over its marginal probability.

Events X and Y happen simultaneously with lesser frequency than if they were independent events.

There is a lack of sufficient information to determine probabilities.

Event A occurs with a probability of 25% given that event B has occurred.

Event A occurs with a certainty when event B occurs.

Event A and B are mutually exclusive events.

Systematic sampling

Cluster sampling

Simple random sampling

Stratified random sampling