probability cheat sheet

P(AUB) = P(A) + P(B) − P(An B). Bayes' Theorem. P(ANB) = 0. Independent. A B. P(BA) · P(A). P(A|B) = P(B). P(A|B). = P(ANB). P(B). P(B|A) = P(A|B) · P(B).

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For convenience, the field of statistics may be divided into three subfields: prob- ability, theoretical statistics, and applied statistics. ... Reference Manual ...

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Probability is a branch of mathematics that deals with calculating the likelihood of a given event's occurrence, which is expressed as a number between 0 and 1.

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The following formula is used to calculate the expected value: Expected V alue = P (A) ⇥ (P rofit/Loss from A) + P (B) ⇥ (P rofit/Loss ...

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Probability Mass Function (PMF) (Discrete Only) gives the probability that a random variable takes on the value X. PX (x) = P (X = x).

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The collection of all probability distributions for different values of the parameter is called a family of probability distributions. Cumulative Distribution ...

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The second set of branches in a tree diagram represent the conditional probabilities. Example 2: In a tennis match, the probability that Anne wins the first set.

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When the chance of one event occurring is dependent on another event occurring, these events are not independent, and the probability is calculated differently.

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Probability theory is the study of uncertainty. Through this class, we will be relying on concepts from probability theory for deriving machine learning ...

cs229.stanford.edu·285.5 KB

TI-84+ Quick Reference Sheet AP Statistics. To Get Scatter Plots and Regressions. (Linear, Quadratic, Exponential, Power, etc). 1. Place data in Lists: STAT → ...

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The averaging argument: let X be a random variable and µ = E[X] be its expectation. Then, X gets some value a ≥ µ with a positive probability (and the same goes ...

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The conditional probabilities are P(Ak|H1)=1 for any k, and P(Ak|H2)=1/2k. By total probability formula,. P(Ak) = 2k + N − 1. 2kN. ,.

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There will be three questions: one will be mostly based around the normal distribution, one around probability trees, and one around two-way tables.

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Events A and B are independent if probability of A given B equals probability of A. Dependent events (or non-independent events): Events that are not ...

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Review of “English translation” for events: • A ∩ B = “both events A and B happen”. • A ∪ B = “either event A or B (or both) happens”.

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What do you need for stats to be informative? • An appropriate sample. • Variability in the data. • Good study methodology. Key Evaluation ...

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Probability Cheat Sheet. • P(Ac)=1 − P(A). • P(A ∪ B) = P(A) + P(B) if A, B do not overlap. • P(A ∩ B) = P(A)P(B) if A, B are independent. • E(aX + bY + c) ...

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Learning Target: Understand how the probability of an event indicates its likelihood. Success Criteria: • I can identify possible outcomes of an experiment. • I ...

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