Qm 214 5.1 & 5.2 & 5.4

Random variable-

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

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.

Risk-neutral consumer-

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

Risk-loving consumer-

Someone who may accept a risky prospect even if the expected gain is negative.

Binomial random variable-

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

Probability mass function-

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

A BERNOULLI PROCESS

There are only two possible outcomes, conventionally labeled success and failure; and The probabilities of success and failure remain the same from trial to trial.

The expected value of the discrete random variable X is

a weighted average of all possible values of X.

Which of the following are examples of discrete random variables?

1. The number of students who earn an "A" on their statistics exam 2. The number of people who vote for the Democratic Party candidate in the next presidential election

Which of the following represents the expected value?

E(X) μ

Generally, a person who is risk neutral

bases decisions solely on the basis of expected values.

The results of a Bernoulli process is a

binomial distribution

If X is a binomial random variable, then E(X)=

μ np

Binomial distribution-

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

Probability tree-

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

Which of the following are conditions of a binomial experiment (Bernoulli process)?

Each trial is independent of the previous trial. Each trial has only two possible outcomes, often labeled 'success' and 'failure'. For each trial, the probabilities of 'success' and 'failure' remain the same.

The population mean is also referred to as the

expected value

Cumulative distribution function-

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

Bernoulli process-

A series of n independent and identical trials of an experiment such that each trial has only two possible outcomes, and each time the trial is repeated, the probabilities of success and failure remain the same.

Discrete uniform distribution-

A symmetric distribution where the random variable assumes a finite number of values and each value is equally likely.

Discrete (random) variable-

A variable that assumes a countable number of values.

Continuous (random) variable-

A variable that assumes uncountable values in an interval.

Expected value-

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

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.

Which of the following are used to indicate whether the values of X are clustered about μ or widely scattered from μ?

Standard deviation σ2 σ Variance

True or false: A discrete random variable X may assume an (infinitely) uncountable number of distinct values.

false

Consumers are said to be risk-averse

if they care about risk and, if confronted with two choices with the same expected gains, they prefer the one with lower risk.