Flashcards in 4 - Probability Deck (31):

1

## Probability is ______, based on ______ rather than ______.

### Empirical; observations; theory

2

## How does random sampling differ from a random phenomenon?

###
Random sampling: every individual in a population has the same chance of being selected.

Random phenomenon: does not necessarily mean that each outcome is equally likely, just that the outcomes are determined by CHANCE.

3

## A phenomenon is random if: _____.

### Individual outcomes are uncertain, but there is nonetheless a regular distribution of outcomes in a large # of repetitions.

4

## What is the probability of a random phenomenon?

### The proportion of times the outcome would occur in a very long series of repetitions.

5

## The frequentist approach to defining probabilities:

### The idea that probability describes only what will happen in the long run.

6

## What does it mean to say that something is "random"?

### That we cannot know in advance what the outcome may be. We can predict the likelihood, but we cannot know for certain until it happens.

7

## Probability definition

### A number between 0 and 1 that describes the likelihood of a random event occurring

8

## The sum of the probabilities for all outcomes of a random event must equal ___.

### 1

9

## Probability of event formula

### Probability of event = # of ways an event could occur/# of possible outcomes

10

## Something is _____ if we cannot know the outcome in advance.

### Random

11

## Sample space (S)

### S of a random phenomenon is the set of all possible outcomes

12

## A _______ is a subset of a sample space.

### Event

13

## Event

### An outcome, or a set of outcomes of a random phenomenon. A subset of a sample space.

14

## What 2 things does a probability model consist of?

###
1. A sample space (S)

2. A way of assigning probabilities to events

15

## Two events that have no events in common, and cannot occur simultaneously

### Disjoint events (mutually exclusive)

16

## An example of a disjoint event

### Having a baby - it can be either male or female.

17

## Discrete probability model

### A probability model made up of a list of individual outcomes. All of the probabilities within the sample space must sum to 1.

18

## How can you tell if a probability model is discrete?

### All probabilities sum to 1.

19

## What will the sample space be in a continuous probability model?

### An interval of numbers (i.e. S = {all numbers between 0 and 1}

20

## A model for a continuous distribution

### Density curve

21

## Area under a density curve

###
Always = 1.

This corresponds to a probability of 1.

22

## Can a set of real data ever be actually described by a density curve?

### No. It is an idealized model.

23

## The median of a density curve is the _________.

### Equal areas point.

24

## The mean of a density curve is the _________.

### Point at which the curve would balance of made of solid material of varying weight.

25

## Random variable definition

### A variable whose value is a numerical outcome of a random phenomenon. We know it is random if its value changes from one random choice to another.

26

## Independent

### The outcome of the first event cannot influence the outcome of the second event.

27

## Multiplication rule for independent events.

### P(A and B) = P(A)*P(B)

28

## The multiplication rule holds for _________.

### Independent events.

29

## The addition rule holds for _________.

### Disjoint events.

30

## What does "|" mean in conditional probability? i.e. P(X|Y)

### It means "given the information that"

31