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Combinatorial Description and Free Convolution
Combinatorial Description and Free Convolution

4. Random Variables, Bernoulli, Binomial, Hypergeometric
4. Random Variables, Bernoulli, Binomial, Hypergeometric

... probability that the 2 of them are red? Now suppose that you draw 5 jelly beans out of the bag. What is the probability that 3 are red and 2 are green? This is an example of a Hypergeometric random variable. The characteristic is “being red”. The population is the jelly beans in the bag, so N = 10. ...
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...  Independent events: either A & B has no effect on the other Example: event A: die 16, event B: die 24, P(A)=1/6, P(B)=1/6, two independent events, P(A and B)= P(A)P(B)=(1/6)(1/6)=1/36  Mutual exclusive: outcome of A will exclude outcome of B and vice versa  Joint probability  both A & B occur ...
Mathematics Department, NUI Galway
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... Independent Events - events where the occurrence or nonoccurrence of one does not change the probability that the other will occur. For example: You select a card at random, record it, and then place it back in the deck. Since you replaced it, the probabilities when you select the 2nd card do not ch ...
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... Ex) Three shirts, 4 pairs of pants, and 2 pairs of shoes. How many outfits are possible? Try) 3 dice are rolled ...
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... There are two fundamental but very different approaches to statistical analysis: the Bayesian and frequentist techniques. The former is named after the 18th-century English theologian and mathematician Thomas Bayes (see the book review on page 54 of this issue). The two approaches differ in their in ...
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... There are two possible ways to frame a causal reasoning problem. As formalized by Fernbach, Darlow, and Sloman (2011), a predictive probability judgment is represented by the conditional probability p(Effect | Cause) and a diagnostic probability judgment is represented by the conditional probability ...
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Creating Probability Models for Simple Events

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Indeterminism

Indeterminism is the concept that events (certain events, or events of certain types) are not caused, or not caused deterministically (cf. causality) by prior events. It is the opposite of determinism and related to chance. It is highly relevant to the philosophical problem of free will, particularly in the form of metaphysical libertarianism.In science, most specifically quantum theory in physics, indeterminism is the belief that no event is certain and the entire outcome of anything is a probability. The Heisenberg uncertainty relations and the “Born rule”, proposed by Max Born, are often starting points in support of the indeterministic nature of the universe. Indeterminism is also asserted by Sir Arthur Eddington, and Murray Gell-Mann. Indeterminism has been promoted by the French biologist Jacques Monod's essay ""Chance and Necessity"". The physicist-chemist Ilya Prigogine argued for indeterminism in complex systems.
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