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Probability in Machine Learning Cheat Sheet

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Probability in Machine Learning Cheat Sheet

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Questions and Answers

What is the definition of a sample space?

The set of all possible outcomes, with mutually exclusive and collectively exhaustive elements (correct)

The set of all possible outcomes, with dependent and exhaustive elements

The set of all possible outcomes, with mutually exclusive and non-exhaustive elements

The set of all impossible outcomes, with mutually exclusive and collectively exhaustive elements

What are the axioms of probability?

$P(A) extgreater= 0$, $P(A_i)P(B extbar A_i) extless extgreater j P(A_j)P(B extbar A_j)$, $P(A extintercal B) = P(A)P(B)$ (correct)

$P(A) = 1$, $P(A_i)P(B extbar A_i) extsum j P(A_j)P(B extbar A_j)$, $P(A extintercal B) = P(A)P(B)$

$P(A) extgreater 0$, $P(A_i)P(B extbar A_i) extsum j P(A_j)P(B extbar A_j)$, $P(A extintercal B) = P(A)P(B)$

$P(A) extgreater= 0$, $P(A_i)P(B extbar A_i) extsum j P(A_j)P(B extbar A_j)$, $P(A extintercal B) extgreater P(A)P(B)$

What is the corollary related to independent events?

If A and B are independent, then A and $B^c$ are independent (correct)

If A and B are dependent, then A and $B^c$ are dependent

If A and B are independent, then A and $B^c$ are dependent

If A and B are dependent, then A and $B^c$ are independent

What is the probability of the empty set?

<p>$P( extemptyset) = 0$</p> Signup and view all the answers

How is the probability of a union of disjoint events calculated?

<p>$P(igcup A_i ) = extsum P(A_i)$</p> Signup and view all the answers

Study Notes

Sample Space and Probability Axioms

A sample space is a set of all possible outcomes of an experiment, denoted by Ω (Omega) and is usually represented by the set of all possible outcomes.

Axioms of Probability

The probability of an event is a non-negative real number, denoted by P(E) ≥ 0.
The probability of the sample space is equal to 1, P(Ω) = 1.
The probability of the union of a countable number of disjoint events is the sum of their individual probabilities.

Independent Events

The corollary of independent events states that if A and B are independent events, then P(A ∩ B) = P(A) × P(B).

Empty Set and Union of Disjoint Events

The probability of the empty set is 0, P(∅) = 0.
The probability of a union of disjoint events A and B is calculated by P(A ∪ B) = P(A) + P(B).

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Description

Test your knowledge of probability in machine learning with this cheat sheet quiz. It covers topics such as Bayes' rule, conditional probabilities, probability models, and axioms.