The course covers the probability, distribution theory and statistical inference needed for advanced courses in statistics and econometrics. Michaelmas term: Probability. Conditional probability and ...

The idea of conditional probability can be used to provide a general representation of a joint distribution as a product, but a more complicated product than arises with an iid vector. As one would ...

Conditional probability occurs when it is given that something has happened. (Hint: look for the word “given” in the question. The probability that a tennis player wins the first set of a ...

Studies axioms, counting formulas, conditional probability, independence, random variables, continuous and discrete distribution, expectation, joint distributions, moment generating functions, law of ...

The probability that a tennis player wins the first set of a match is \(\frac{3}{5}\). If she wins the first set, the probability that she wins the second set is \(\frac{9}{10}\). If she loses the ...

Studies axioms, counting formulas, conditional probability, independence, random variables, continuous and discrete distribution, expectation, joint distributions, moment generating functions, law of ...

The basic theory is developed in §9.1. In §9.2 I apply the theory to prove the existence of regular conditional probability distributions, and in §9.3 I use it to derive Donsker’s Invariance Principle ...