PROBABILITY AND STATISTICS

1. Events and logic operations between events.

2. Setting axiomatic probability, classical definition of probability, the frequentist approach, subjective approach, the criterion of the bet, property of the probability.

3. Simple random numbers, prevision of a simple random number. Variance of a simple random number, covariance. Variance of sums and differences of random numbers, the correlation coefficient, properties, linear dependence.

4. Conditioned events and conditional probabilities.

5. Stochastic independence. exchangeable events. Exchangeability and frequentist setting. Extractions with and without a refund from an urn of known composition, binomial and hypergeometric distribution, properties, prevision and variance. Extractions of unknown composition polls, mixtures of binomial and hypergeometric distributions. Bayes' theorem, meaning inference, likelihood values.

6. Discrete random numbers, previsionand distribution function of discrete random variables. Major distributions of discrete random variables.

7. Absolutely continuous random variables, density and distribution functions. Prevision and variance of continuous random variables. Major distributions of absolutely continuous random variables.

8. Discrete random vectors, marginal and conditional distributions, relationship between the joint distribution and marginal, stochastic independence, relationship with the incorrelation properties. Multinomial distribution.

9. Random vectors continuous, cumulative distribution function and joint probability density, marginal and conditional distributions, stochastic and incorrelation independence, probability distribution of the maximum and minimum of two random numbers, application to the case of exponential distributions. Sums of independent random variables and not, convolution integral.

10. Conditional Distributions. Generating function. Characteristic function.

11. Stochastic Processes. Bernoulli's process. Problem of gambler's ruin.

Incertezza e Probabilita' - Scozzafava Romano - Zanichelli