Chapter 14: Randomness and Probability

Binomial Model

P(X = x) =

variance

the variance of a random variable is the expected value of the squared deviations from the mean. For descrete random variables, it can be calculated as: Var(X)

Bernoulli Trials

A sequence of trials are called Bernoulli trials if: 1. There are exactly two possible outcomes (usually denoted success and failure) 2. The probability of success is constant 3. The trials are independent

continuous random variable

a random variable that can take on any of an (uncountably) infinite number of outcomes

random variable

assumes any of several different values as a result of some random event. Random variables are denoted by a capital letter, such as X

The length of time the battery in a cell phone lasts before needing charging is a (discrete/continuous) random variable

continuous

The zip code of a randomly selected person in the US is a (discrete/continuous) random variable

discrete

Binomial probability distribution

a binomial distribution is appropriate for a random variable that counts the number of successes in n Bernoulli trials

Poisson Model

a discrete model often used to model the number of arrivals of events such as customers arriving in a queue or calls arriving into a call center

probability model

a function that associates with a probability P with each value of a discrete random variable X, denoted P(X = x) or P(x), or with any intervale of values of a continuous random variable

discrete random variable

a random variable that can take one of a finite number of distinct outcomes

Standard deviation of a random variable

describes the spread in the model and is the square root of the variance, denoted SD(X)

The baseball hat size of a randomly chosen student in your statistics class is a (discrete/continuous) random variable

discrete

the probability model for the sum of two random variables is the same as the model for the individual random variables

false

the variance of the sum of two random variables, Var(X+Y), is the sum of the variances, Var(X) + Var(Y)

false

expected value

the expected value of a random variable is its theoretical long-run average value, the center of its model. Denoted E(X), it is found (if the random variable is discrete) by summing the products of variable values and probabilities

Which of the following are random variables? A. The shoe size of a randomly selected person in your statistics class B. The sum of two rolled dice in a gambling game such as craps C. Whether the stoplight at a street corner is red or​ green, with 1=red and 2=green D. The closing price of a particular stock E. All of the above

E. All of the above

The expected value of the sum of two random​ variables, E(X+Y)​, is the sum of the expected​ values, E(X)+E(Y). True/False

True

The sum of two Normal random variables is still a Normal random variable. True/False

True