- Compare “Frequentist probability” vs. “Bayesian probability”?
- What is a random variable?
- What is a probability distribution?
- What is a probability mass function?
- What is a probability density function?
- What is a joint probability distribution?
- What are the conditions for a function to be a probability mass function?
- What are the conditions for a function to be a probability density function?
- What is a marginal probability? Given the joint probability function, how will you calculate it?
- What is conditional probability? Given the joint probability function, how will you calculate it?
- State the Chain rule of conditional probabilities.
- What are the conditions for independence and conditional independence of two random variables?
- What are expectation, variance and covariance?
- Compare covariance and independence.
- What is the covariance for a vector of random variables?
- What is a Bernoulli distribution? Calculate the expectation and variance of a random variable that follows Bernoulli distribution?
- What is a multinoulli distribution?
- What is a normal distribution?
- Why is the normal distribution a default choice for a prior over a set of real numbers?
- What is the central limit theorem?
- What are exponential and Laplace distribution?
- What are Dirac distribution and Empirical distribution?
- What is mixture of distributions?
- Name two common examples of mixture of distributions? (Empirical and Gaussian Mixture)
- Is Gaussian mixture model a universal approximator of densities?
- Write the formulae for logistic and softplus function.
- Write the formulae for Bayes rule.
- What do you mean by measure zero and almost everywhere?
- If two random variables are related in a deterministic way, how are the PDFs related?
- Define self-information. What are its units?
- What are Shannon entropy and differential entropy?
- What is Kullback-Leibler (KL) divergence?
- Can KL divergence be used as a distance measure?
- Define cross-entropy.
- What are structured probabilistic models or graphical models?
- In the context of structured probabilistic models, what are directed and undirected models? How are they represented? What are cliques in undirected structured probabilistic models?
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Probably theory is the foundation of every aspect of quantitative finance