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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

Addition probability rule

P(A or B) = P(A) + P(B) - P(A and B)