AMuch of the Probability and Statistics You Need
A.1 Probability Distributions and Their Properties
When a well-defined and measurable thing
is uncertain, with a number of ways
could turn out, it defines a random variable (r.v.). Each outcome or realization has a probability
. The function that assigns a probability to each possible outcome of the r.v.
is called a probability distribution. One of them is actually going to happen, so probabilities
of all the possible outcomes
add up to exactly 1. If the outcomes can be counted, we have a discrete probability distribution. If the possible outcomes lie on a continuum, encompassing all, an interval or a segment of the real numbers, it’s a continuous probability distribution.
Events are combinations of outcomes, for example, an asset price falling on one day and rising the next or a firm not defaulting this year and also not defaulting ...
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