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I have a choice between two courses: Analysis 1 and "Honours Probability". The target syllabus of the probability class is:
Sample space, set operations, the Kolmogorov axioms and basic consequences. Probability on finite sample spaces. Conditional probability, independent events, the law of total probability, Bayes Theorem. Random variables, discrete and continuous univariate distributions. The discrete uniform, hypergeometric, binomial, Poisson, uniform, gamma, exponential, chi-square, beta and normal distributions. Moments, basic inequalities, generating functions and transformations in one dimension. Multivariate distributions, independence. The multinomial and multivariate normal distributions. Covariance and correlation. Conditional distributions, conditional expectation Modes of convergence, the Strong and Weak Laws of Large Numbers, the Central Limit Theorem.
Which course would you recommend for a physics undergrad?
Sample space, set operations, the Kolmogorov axioms and basic consequences. Probability on finite sample spaces. Conditional probability, independent events, the law of total probability, Bayes Theorem. Random variables, discrete and continuous univariate distributions. The discrete uniform, hypergeometric, binomial, Poisson, uniform, gamma, exponential, chi-square, beta and normal distributions. Moments, basic inequalities, generating functions and transformations in one dimension. Multivariate distributions, independence. The multinomial and multivariate normal distributions. Covariance and correlation. Conditional distributions, conditional expectation Modes of convergence, the Strong and Weak Laws of Large Numbers, the Central Limit Theorem.
Which course would you recommend for a physics undergrad?