Statistics 6.1

Determine whether the random variable is discrete or continuous. In each​ case, state the possible values of the random variable. ​(a) The number of hits to a Web site in a day.

​(a) Is the number of hits to a Web site in a day discrete or​ continuous? The random variable is discrete. The possible values are x=0, 1, 2,......

Discrete Random Variable

A discrete random variable has either a finite or countable number of values. The values of a discrete random variable can be plotted on a number line with space between each point.

Random variable

A random variable is a numerical measure of the outcome of a probability experiment, so its value is determined by chance. Random variables are typically denoted using capital letters such as X.

​(b) The square footage of a house.

​(b) Is the square footage of a house discrete or​ continuous? The random variable is continuous. The possible values are a >0

Continuous Random Variable

A continuous random variable has infinitely many values. The values of a continuous random variable can be plotted on a line in an uninterrupted fashion.

An experiment is said to be a binomial experiment provided that the following statements are true.

1. The experiment is performed a fixed number of times. Each repetition of the experiment is called a trial. 2. The trials are independent. This means the outcome of one trial will not affect the outcome of the other trials. 3. For each​ trial, there are two mutually exclusive​ (disjoint) outcomes, success or failure. 4. The probability of success is the same for each trial of the experime

When can the Empirical Rule be used to identify unusual results in a binomial​ experiment? Why can the Empirical Rule be used to identify results in a binomial​ experiment?

The Empirical Rule can only be used to identify results in binomial experiments when certain requirements are met. The Empirical Rule can be used to identify unusual results in a binomial distribution when it is approximately bell shaped because about​ 95% of the outcomes are in the interval from ir - 2 sigma to ir + 2 sigma. The Empirical Rule can be used to identify results in binomial experiments when no left parenthesis 1 minus p right parenthesis greater than or equals 10

State the conditions required for a random variable X to follow a Poisson process.

The probability of success is the sme for aany two intervals of equal length. The probability of two or more successes in any sufficiently small subinterval is 0. The number os successes in any interval is independent of the number of successes in any other interveal provided the intervas are not overlapping.

Is the time required to download a file from the Internet discrete or​ continuous?

The random variable is continuous. The possible values are t greater than 0.

(c) Is the time it takes to fly from City A to City B discrete or continuous?

The random variable is continuous. The possible values are t>0.

Is the number of people in a restuarant that has a capacity of 300 discrete or​ continuous?

The random variable is discrete. The possible values are x = ​0, 1, ​2,...comma 300