Probability distributions form the foundation for understand most statistics taught at the MBA and CFA courses. Both descriptive and inferential statistics draw on the understanding of distributions and test the understanding of common probability distributions at different levels. Graduate Tutor’s statistics tutors can provide live online tutoring to help you understand the common probability distributions, its properties and underlying assumptions.
According to the CFA Institute, after assimilating information on common probability distributions, a candidate should be able to:
- define a probability distribution and distinguish between discrete and continuous random variables and their probability functions;
- describe the set of possible outcomes of a specified discrete random variable;
- interpret a cumulative distribution function;
- calculate and interpret probabilities for a random variable, given its cumulative distribution function;
- define a discrete uniform random variable, a Bernoulli random variable, and a binomial random variable;
- calculate and interpret probabilities given the discrete uniform and the binomial distribution functions;
- construct a binomial tree to describe stock price movement;
- calculate and interpret tracking error;
- define the continuous uniform distribution and calculate and interpret probabilities, given a continuous uniform distribution;
- explain the key properties of the normal distribution;
- distinguish between a univariate and a multivariate distribution and explain the role of correlation in the multivariate normal distribution;
- determine the probability that a normally distributed random variable lies inside a given interval;
- define the standard normal distribution, explain how to standardize a random variable, and calculate and interpret probabilities using the standard normal distribution;
- define shortfall risk, calculate the safety-first ratio, and select an optimal portfolio using Roy’s safety-first criterion;
- explain the relationship between normal and lognormal distributions and why the lognormal distribution is used to model asset prices;
- distinguish between discretely and continuously compounded rates of return and calculate and interpret a continuously compounded rate of return, given a specific holding period return;
- explain Monte Carlo simulation and describe its applications and limitations;
- compare Monte Carlo simulation and historical simulation.
You can test your understanding of the common probability distributions using this quiz.