Probability distributions

Probability distributions determine how the values of random variables are spread. For example, the set of all the possible outcomes of the tossing of a sequence of coins gives rise to binomial distribution. The means of large samples of the data population follow normal distribution, which is the most common and useful distribution.

The features of these distributions are very well known and can be used to extract inferences about the population. We are going to discuss in this chapter some of the most common probability distributions and how to compute them.

Normal distribution

Normal distribution is the most widely used probability distribution in the financial industry. It is a bell-shaped curve and mean, median mode is the same for normal distribution. It is denoted by  where  is the mean and  is the variance of the sample. If the mean is 0 and variance is 1 then the normal distribution is known as standard normal distribution N(1, 0).

Now let...