Roteiro:
Probabilidades e Estatística

Prof. Francisco A. Rodrigues

Instituto de Ciências Matemáticas e de Computação

Universidade de São Paulo

· Livros de Probabilidades online:

o Introduction to Probability, Statistics and Random Processes, https://www.probabilitycourse.com

o Introduction to Probability for Data Science, https://probability4datascience.com

o Machine Learning: a Probabilistic Perspective, https://probml.github.io/pml-book

o Probability and Statistics, http://www.utstat.toronto.edu/mikevans/jeffrosenthal/book.pdf

o Introduction to Probability, https://drive.google.com/file/d/1VmkAAGOYCTORq1wxSQqy255qLJjTNvBI/view

· Aula 1: Introdução à Teoria das Probabilidades

https://www.youtube.com/watch?v=7aHjkGFtbnM&list=PLSc7xcwCGNh3Ls-WARhH54WwiqB91Kyak&t=0s&ab_channel=FranciscoRodrigues

Suplementar: Probabilidade no lançamento de dados

https://pt.khanacademy.org/math/precalculus/prob-comb/independent-events-precalc/v/events-and-outcomes-2

Suplementar: Probabilidade com diagramas de Venn

https://pt.khanacademy.org/math/precalculus/prob-comb/addition-rule-prob-precalc/v/probability-with-playing-cards-and-venn-diagrams

· Aula 2: Probabilidade Condicional e Independência

https://www.youtube.com/watch?v=HzOCwzzlGiA&list=PLSc7xcwCGNh3Ls-WARhH54WwiqB91Kyak&index=3&ab_channel=FranciscoRodrigues

Exemplos:

https://www.youtube.com/watch?v=zg1-EvSWqlw&ab_channel=KhanAcademyBrasil

https://www.youtube.com/watch?v=LYIoWcrrffs&ab_channel=KhanAcademyBrasil

https://pt.khanacademy.org/math/statistics-probability/probability-library/conditional-probability-independence/v/calculating-conditional-probability

https://www.youtube.com/watch?v=gAaqxWgk2UM&ab_channel=KhanAcademyBrasil

· Aula3: Teorema de Bayes

https://www.youtube.com/watch?v=sRfVDPJAkro&list=PLSc7xcwCGNh3Ls-WARhH54WwiqB91Kyak&index=4&ab_channel=FranciscoRodrigues

https://www.youtube.com/watch?v=q8f9HeUaPbE&list=PLSc7xcwCGNh3Ls-WARhH54WwiqB91Kyak&index=4&ab_channel=FranciscoRodrigues

Simulação do problema de Monty-Hall:

https://github.com/franciscoicmc/simulacao/blob/master/Monty-Hall.ipynb

Vídeo sobre o teorema de Bayes do Veritasium:

https://www.youtube.com/watch?v=R13BD8qKeTg

· Aula 4: Variáveis aleatórias

https://www.youtube.com/watch?v=qN_K0NuJPs8&list=PLSc7xcwCGNh3Ls-WARhH54WwiqB91Kyak&index=5&ab_channel=FranciscoRodrigues

Exemplo na Khan Academy:

https://pt.khanacademy.org/math/statistics-probability/random-variables-stats-library/random-variables-discrete/v/random-variables

· Aula 5: Função de distribuição

https://www.youtube.com/watch?v=Nbq0DWW26ag&list=PLSc7xcwCGNh3Ls-WARhH54WwiqB91Kyak&index=5&ab_channel=FranciscoRodrigues

https://www.youtube.com/watch?v=0T-hG7YOtIo&t=731s&ab_channel=FranciscoRodrigues

· Aula 6: Valor esperado e variância

https://www.youtube.com/watch?v=6_6Ek8q1bDE&list=PLSc7xcwCGNh3Ls-WARhH54WwiqB91Kyak&index=8&ab_channel=FranciscoRodrigues

https://www.youtube.com/watch?v=0g9mGVPNnR0&list=PLSc7xcwCGNh3Ls-WARhH54WwiqB91Kyak&index=9&ab_channel=FranciscoRodrigues

· Aula 7: Valor esperado e variância (continuação)

https://www.youtube.com/watch?v=kXArrVxPcno&list=PLSc7xcwCGNh3Ls-WARhH54WwiqB91Kyak&index=8&ab_channel=FranciscoRodrigues

https://www.youtube.com/watch?v=XiTL_rWUB0U&list=PLSc7xcwCGNh3Ls-WARhH54WwiqB91Kyak&index=9&ab_channel=FranciscoRodrigues

· Aula 8: Distribuições Uniforme discreta, Bernoulli e Binomial

https://www.youtube.com/watch?v=zKlRBfVGsyM&list=PLSc7xcwCGNh3Ls-WARhH54WwiqB91Kyak&index=11&ab_channel=FranciscoRodrigues

Simulação em Python:

https://github.com/franciscoicmc/simulacao/blob/master/distribuicao-binomial.ipynb

· Aula 9: Distribuição de Poisson

https://www.youtube.com/watch?v=4b9ShYWAows&list=PLSc7xcwCGNh3Ls-WARhH54WwiqB91Kyak&index=12

Vídeo da Khan Academy:

https://pt.khanacademy.org/math/statistics-probability/random-variables-stats-library/poisson-distribution/v/poisson-process-1

Simulação em Python:

https://github.com/franciscoicmc/simulacao/blob/master/distribuicao-Poisson.ipynb

· Aula 10: Distribuição geométrica, binomial negativa e hipergeométrica

https://www.youtube.com/watch?v=Ke9dn-cSXow&list=PLSc7xcwCGNh3Ls-WARhH54WwiqB91Kyak&index=12&ab_channel=FranciscoRodrigues

Simulação em Python:

https://github.com/franciscoicmc/simulacao/blob/master/distribuicao-geometrica.ipynb

https://github.com/franciscoicmc/simulacao/blob/master/distribuicao-hipergeometrica.ipynb

· Aula 11: A distribuição Normal (Gaussiana)

https://www.youtube.com/watch?v=jdcKU2sgDfg&list=PLSc7xcwCGNh3Ls-WARhH54WwiqB91Kyak&ab_channel=FranciscoRodrigues

Aproximação da binomial pela normal:

https://www.youtube.com/watch?v=CCqWkJ_pqNU&ab_channel=jbstatistics

Simulação em Python:

https://github.com/franciscoicmc/simulacao/blob/master/dist-normal.ipynb

· Aula 12: Modelos Contínuos: Exponencial, Uniforme, Gama, Beta, Weibull e t-student

https://www.youtube.com/watch?v=crumAouFNRE&list=PLSc7xcwCGNh3Ls-WARhH54WwiqB91Kyak&index=14&ab_channel=FranciscoRodrigues

Distribuição Gama:

https://www.youtube.com/watch?v=J0Yzmb_PY3Y&ab_channel=Oxeduc

Distribuição Beta:

https://www.youtube.com/watch?v=v1uUgTcInQk&ab_channel=Oxeduc

· Aula 13: Simulação de Monte Carlo

https://www.youtube.com/watch?v=rNOe62Z3zZg&ab_channel=FranciscoRodrigues

Simulação em Python:

https://github.com/franciscoicmc/simulacao/blob/master/Simulacao.ipynb

· Aulas 14: Variáveis Aleatórias Multidimensionais

https://www.youtube.com/watch?v=k5A-wUXi9dQ&t=12s&ab_channel=FranciscoRodrigues

· Aula 15: Variáveis aleatórias: Probabilidade Condicional

https://www.youtube.com/watch?v=6jiMtSaIj88&ab_channel=FranciscoRodrigues

· Aula 16: Esperança condicional

https://www.youtube.com/watch?v=eKQXI1U2UQ0&list=PLSc7xcwCGNh3Ls-WARhH54WwiqB91Kyak&index=17&ab_channel=FranciscoRodrigues

· Aula 17: Função geratriz de momentos

https://www.youtube.com/watch?v=7UfbwBBlCYc&t=18s&ab_channel=FranciscoRodrigues

· Aula 19: Teorema Central do Limite

https://www.youtube.com/watch?v=QcQz6_93GC4&list=PLSc7xcwCGNh3Ls-WARhH54WwiqB91Kyak&index=18&ab_channel=FranciscoRodrigues

Prova do Teorema Central do Limite

https://www.youtube.com/watch?v=aJcyQjskvqo&list=PLSc7xcwCGNh3Ls-WARhH54WwiqB91Kyak&index=19&ab_channel=FranciscoRodrigues

Simulação em Python:

https://github.com/franciscoicmc/simulacao/blob/master/Teorema-Central-do-Limite.ipynb

· Aula 20: Desigualdades importantes

https://www.youtube.com/watch?v=ZvzJ74_f538&t=40s

· Aula 21: Estimação por máxima verossimilhança

Em elaboração...

· Aula 22: Intervalo de Confiança

https://www.youtube.com/watch?v=AkmyfLc-EOs&t=1946s&ab_channel=FranciscoRodrigues

Simulação em Python:

https://github.com/franciscoicmc/simulacao/blob/master/Intervalo-de-confianca.ipynb

· Aula 23: Teste de hipóteses

https://www.youtube.com/watch?v=S3V5qJ1bxhk&ab_channel=FranciscoRodrigues

Simulação em Python:

https://github.com/franciscoicmc/simulacao/blob/master/Teste-de-hipoteses.ipynb

· Aula 24: Cadeias de Markov

Parte 1:

https://www.youtube.com/watch?v=k6FAZJGTZJo&list=PLSc7xcwCGNh0jSylDm0QrDJaFTC3vAbvc&index=2&ab_channel=FranciscoRodrigues

Parte 2:

https://www.youtube.com/watch?v=0ymZ2Iv_9q8&list=PLSc7xcwCGNh0jSylDm0QrDJaFTC3vAbvc&index=4

Caminhas aleatórias

https://www.youtube.com/watch?v=cwhQYqR_Iag&list=PLSc7xcwCGNh0jSylDm0QrDJaFTC3vAbvc

· Aula 25: Teoria da Informação

Em elaboração