Chapter 5 Discrete Probability Distributions

Random Variable

A function that assigns numerical values to the outcomes of an experiment.

Discrete (random) Variable

A variable that assumes a countable number of values.

Discrete Uniform Distribution

A symmetric distribution where the random variable assumes a finite number of values and each value is equally likely. Ex: Figure 5.1 - The distribution has a finite number of specified values. - Each value is equally likely. - The distribution is symmetric.

Properties of Discrete Probability distributions

- the probability of each value between 0 and 1, or equivalent, 0<=P(X=x)<=1. - The same of the probabilities equals 1. In other words. EP(X=xi)=1, where the sam extends over all values x of X.

Portfolio

A collection of assets.

Binomial Probability distribution

A description of the probabilities associated with the possible values of a binomial random variable.

Binomial Distribution

A description of the probabilities with the possible values of a binomial Random variable.

Probability Tree

A graphical representation of the various possible sequences of an experiment.

Cumulative Distribution Function

A probability that the value of a random variable X is less that or equal to a particular value x, P(X<=x).

Discrete VS Continuous Random Variable

A random variable is a function that assigns numerical values to the outcomes of an experiment. A discrete random variable assumes a countable number of distinct values. A continuous random variable, on the other hand, is characterized by uncountable values in an interval.

Bernoulli Process

A series of n independent and identical trails of an experiment such that each trial has only two possible outcomes, and each time the trial is repeated, the probability of success and failure remain the same. - There are only 2 outcomes, success and failure. - The probabilities of success and failure remain the same from trail to trail.

Continuous (random) Variable

A variable that assumes uncountable values in an interval.

Expected Value of a Discrete Random Variable (population mean)

A weighted average of all possible values of a random variable.

Probability Distribution

Every random variable is associated with a probability distribution that describes the variable completely. it is used to compute probabilities associated with the variable.

Variance & Standard Deviation of a Discrete Random Variable

Indicates whether the values of X are clustered about theMean, or widely scattered from the Mean.

Risk Neutral

Someone who is indifferent to risk and makes his/her decisions solely on the bases of the expected gain.

Risk-Averse Consumer

Someone who takes risk only if it entails a suitable compensation and may decline a risky prospect even if it offers a positive expected gain.

Binomial Random Variable

The number of success achieved in the n trials of a Bernoulli process.

Binomial Random Variable

The number of successes achieved in the n trials a Bernoulli process.

Probability Density Function

The probability density function provides the probability that a continuous random variable falls within a particular range of values.

Probability Mass Function

The probability mass function provides the probability that a discrete random variable takes on a particular values.