QBA 237 Chapter 5

Experimental Outcomes of flipping a coin twice

- Head, Head - Head, Tail - Tail, Head - Tail, Tail

Suppose we want to count the number of heads appearing over the five tosses. Does this experiment show the properties of a binomial experiment? What is the random variable of interest?

1) The experiment consists of five identical trials; each trial involves the tossing of one coin. 2) Two outcomes are possible for each trial: a head or a tail. We can designate head a success and tail a failure. 3) The probability of a head and the probability of a tail are the same for each trial, with p = .5 and 1-p=.5. 4) The trials or tosses are independent because the outcome on any one trial is not affected by what happens on other trials or tosses

Properties of Poisson Experiment

1) The probability of an occurrence is the same for any two intervals of equal length. 2) The occurrence or nonoccurrence in any interval is independent of the occurrence or nonoccurrence in any other interval

Properties of a Binomial Experiment

1) the experiment consists of a sequence of n identical trials. 2) Two outcomes are possible on each trial. We refer to one outcomes as a success and the other outcome as a failure. 3) The probability of a success, denoted by p, does not change from trial to trial. 4) The trials are independent

Probability distribution

A description of how the probabilities are distributed over the values of the random variable.

Empirical discrete distribution

A discrete probability distribution for which the relative frequency method is used to assign the probabilities.

Probability function

A function, denoted by f(x), that provides the probability that x assumes a particular value for a discrete random variable.

Expected value

A measure of the central location, or mean, of a random variable.

Variance

A measure of the variability, or dispersion, of a random variable.

Random Variable

A numerical description of the outcome of an experiment.

Discrete uniform probability distribution

A probability distribution for which each possible value of the random variable has the same probability.

Bivariate probability distribution

A probability distribution involving two random variables. A discrete bivariate probability distribution provides a probability for each pair of values that may occur for the two random variables.

Poisson Probability Distribution

A probability distribution showing the probability of x occurrences of an event over a specified interval of time or space.

Hypergeometric probability distribution

A probability distribution showing the probability of x successes in n trials from a population with r successes and N-r failures

Binomial Probability Distribution

A probability distribution showing the probability of x successes in n trials of a binomial experiment.

Continuous random variable

A random variable that may assume any numerical value in an interval or collection of intervals.

Discrete random variable

A random variable that may assume either a finite number of values or an infinite sequence of values.

What values may the random variable assume?

Any positive value (x>0)

Is the random variable discrete or continuous?

Continuous

Is this random variable discrete or continuous?

Discrete

Binomial probability function

The function used to compute binomial probabilities.

Standard deviation

The positive square root of the variance.

Discrete uniform probability function

f(x) = 1 /n

Define a random variable that represents the number of heads occurring on the two tosses

x = number of heads occurring on the two tosses.

Define a random variable that represents the time in minutes required to assemble the product

x = time in minutes to assemble product