Statistics Chapter 5

Probability Mass Function

A discrete random variable X is a list of the values of X with the associated probability, that is, the list of all possible pairs.

Random Variable

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

Discrete Random Variable

Assumes a countable number of distinct values.

Risk Neutral

Completely ignores risk and always accepts a prospect that offers a positive expected gain.

Bernoulli Process

Consists of a series of n independent and identical trials of an experiment such that on each trials: there are only two possible outcomes labels success and failure; and each time the trial is repeated, the probabilities of success and failure remain the same.

Poisson Random Variable

Counts the number of successes over a given interval of time or space.

Continuous Random Variable

Infinitely uncountable values within any interval.

Risk Loving

May accept a risky prospect even if the expected gain is negative.

Risk Averse

May decline a risky prospect even if it offers a positive expected gain.

Binomial Probability Distribution

Shows the probabilities associated with the possible values of the binomial random variable.

Poisson Process

The number of successes within a specified time or space interval equals any integer between zero and infinity, the numbers of successes counted in non-overlapping intervals are independent, and the probability that success occurs in any interval is the the same for all intervals of equal size and is proportional to the size of the interval.

Binomial Random Variable

X is defined as the number of successes achieved in the n trials of Bernoulli process