Chapter 4 Flashcards

1
Q

Probability

A

Mathematics describing random behaviors, measuring chances, and quantifying uncertainties

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2
Q

Random Phenomenon

A

Situation in which we know what possible outcomes could happen but we don’t know which ones will happen until they occur

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3
Q

Trial

A

An attempt or random experiment that generates an outcome (flipping a coin once)

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4
Q

Probability as a long-term frequency

A

The probability of any outcome of a random phenomenon is the proportion of times the outcome would occur in a long series of repeated trials

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5
Q

Long-term frequency example with a fair coin toss

A

If you were to toss a fair coin, say, a million times, you would tend toward getting heads 1/2 the time and tails 1/2 the time. Thus the probability of getting either can be said to be 1/2.

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6
Q

Sample Space

A

Set of all possible outcomes

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7
Q

Dice Sample Space

A

{1,2,3,4,5,6}

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8
Q

Pop quiz example with three questions (C, I) _ _ _

A

2^3 possibilities since there are 2 choices (Correct, Incorrect) for each of the 3 slots. So there are 8 possibilities in all

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9
Q

Event

A

Any outcome or set of outcomes of a random phenomenon; subset of sample space

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10
Q

P(A)

A

Probability of event A

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11
Q

Three Axioms of Probability

A
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12
Q

Enumeration Method

A

Find probability of each individual outcome in sample space and add probabilities of each outcomes event A contains

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13
Q

Classical Method

A

If outcomes are equally likely:

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14
Q

Complement of A

A

All outcomes in sample space not in A

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15
Q

Complement of A Formula

A
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16
Q

Disjoint Events (Mutually Exclusive)

A

A and B are disjoint if they share no common outcomes

17
Q

Disjoint Formula

A

A and B are disjoint if:

18
Q

Independent Events

A

A and B are independent if event A never affects probability of event B and vice versa

19
Q

Independence Formula

A

A and B are independent if:

20
Q

Union of Events

A

The union of A and B are the outcomes that are in A or B

21
Q

Union Formula

A

The union of A and B is found as:

22
Q

How often are events Independent?

23
Q

Independence and Mutual Exclusivity (Disjointness)

A

They are NOT equal; essentially opposite

24
Q

Random Variable

A

A numerical measurement of the outcome of a random phenomenon

25
Probability Distribution
Specifies random variables values and corresponding likelihoods
26
Discrete Random Variable
Takes on discrete values
27
For each value in the discrete distribution
Each probability between 0 and 1 and sum up to 1
28
Mean of random variable
The expected value, average value of the random var
29
Mean/E(X) Formula
30
Standard Deviation
Deviation/spread of random variable
31
Standard Deviation Formula
32
Binomial Distribution
Binary (success/failure) trial with n binary trials following number of successes of probability p
33
Binary Trial
One with two possible outcomes
34
Three Binomial Distribution Conditions
1. Each of n trials must have two possible outcomes 2. Each trial has probability p of success and 1 - p of failure 3. The n trials are independent
35
X ~ Binomial( n , p )
X is binomially distributed with n trials each with success probability p
36
Binomial Distribution Formula
37
Binomial Distribution Mean and Variance