Probability Flashcards

1
Q

What is a sample space?

A

A sample space is a set of point, they are the possible outcomes of a trial.

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2
Q

What is an event

A

An event is a subset of a sample space

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3
Q

What is a probability function

And its properties

A

A probability is a map from events to real numbers such that
1. P(A) ≥ 0 for all events.
2. P(X) = 1
3. If A ∩ B = ∅ for two events A and B then
P(A ∪ B) = P(A) + P(B)

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4
Q

What is a probability mass function

And its properties

A

A probability mass function is a map from points in the sample space to real numbers
such that

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5
Q

How does a probability function relate to a probability mass function?

A
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6
Q

Calculate the probability of event A given all points in sample space have the same probability.

A
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7
Q

What is the binomial coefficient

A
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8
Q

What is the partitian function

A
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9
Q

What is conditional probability (and formula)

A
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10
Q

What is independence (formula)

A
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11
Q

What is conditional independence (formula)

A
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12
Q

What is Bayes’ rule (formula)

A
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13
Q

How does a naïve Bayes estimator work

A
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14
Q

What is a random variable

A

A random variable is a map from sample space to a set of numerical values

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15
Q

How to calculate P(X=x)

A
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16
Q

What is a probability distribution

A

A probability distribution is a table of probabilities for a random variable.

17
Q

What are joint, conditional and marginal distributions?

18
Q

How to calculate the expected value of a function

19
Q

What is the mean

20
Q

What is the varience

21
Q

What is the nth moment

22
Q

Properties of expected values (multiplication, addition, identity)

23
Q

How to calculate varience using the 2nd moment and square of mean

24
Q

What determines an event to be part of the Poisson process?

25
What is the Poisson distribution (and formula)
26
What is the distribution function
27
What is the density function (in relation to distribution function)
28
Determine distribution function from density function
29
Determine distribution function between 2 values
30
What does the Gauss/Normal distribution look like?
31
What is the density function for the Gauss Distribution
32
How to work out pobabilities of the Gauss distribution
33
Sum of a geometric series (and infinite) formula
34
Binomial distribution formula
35
Mean and varience of binomial distribution
Mean: np Varience np(1-p) or npq
36
How to derive mean and varience of binomial distribution