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Chapter 3: Problem 15

For each of the following exercises, determine the range (possible values) of the random variable. A Web site contains 100 interconnected pages. The random variable is the number of unique pages viewed by a visitor to the Web site.

Short Answer

Expert verified
The range is from 0 to 100.

Step by step solution

01

Understanding the Scenario

We have a website with 100 interconnected pages, and a visitor may view a certain number of these pages. Our task is to determine the range of the random variable, which represents the number of unique pages viewed by a visitor.
02

Identify the Minimum Value

The minimum number of unique pages that a visitor can view is 0, which would occur if they visit the website but do not view any page, or if the website is counted before the first page access.
03

Identify the Maximum Value

The maximum number of unique pages a visitor can view is 100, which happens when the visitor views all the pages on the website.
04

Determine the Range of the Random Variable

The range of the random variable is determined by the minimum and maximum values. Given that the minimum is 0 and the maximum is 100, the range of the random variable is the set of all integers from 0 to 100.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Random Variables
In the world of statistics, a random variable is a variable whose possible values are numerical outcomes of a random phenomenon. When dealing with a website, each visitor鈥檚 behavior can be viewed as a random phenomenon. For the exercise given, the random variable is the number of unique pages a visitor views on a website.
  • Discrete Random Variables: These can take on a countable number of values, such as 0, 1, 2... up to 100 in our case with webpage views.
  • Continuous Random Variables: These take on an infinite number of values within a given range and are not pertinent in this scenario.
It's important to determine the range of the random variable to understand all potential outcomes. In our case, the range is from 0 (no pages viewed) to 100 (all pages viewed). Understanding random variables helps in making calculable predictions and informed decisions.
Probability
Probability is the study of how likely an event is to occur. It provides the foundation for predicting future events or understanding complex phenomena.
In the context of the exercise, probability can help us determine the likelihood of a visitor viewing a certain number of unique pages.
  • Basic Probability: If every page view scenario from 0 to 100 is equally likely, each scenario would have a probability of 1/101.
  • Conditional Probability: Often, some scenarios are more probable based on user behavior, such as spending more time on popular pages.
  • Application in Analytics: Understanding probability in web analytics can guide strategic decisions to improve user experience.
Probability helps allocate resources effectively and create targeted content that aligns with the user journey.
Website Traffic Analytics
Website traffic analytics is the process of tracking and analyzing online traffic to your web pages. It gives you valuable insights into visitor behavior and how they interact with the website's content.
For our random variable of unique page views, analytics can show:
  • Visitor Patterns: Determine how often visitors return and which pages they view the most.
  • Page Performance: Identify which pages are most engaging and which ones may need improvement.
  • Conversion Monitoring: Track how interactions translate into actions like sign-ups, purchases, or inquiries.
These insights not only help in optimizing the website for better performance but also enhance visitor experience by tailoring the website to meet visitor needs.
Unique Page Views
Unique page views refer to the number of distinct visitors that view one or more particular pages on a website. Unlike total page views, which count all visits including repeated visits by the same user, unique page views count each user only once during a session.
For example, if a user accesses a page multiple times in one visit, it counts as one unique view.
  • Importance of Unique Views: They provide a more accurate measure of how many individuals are engaging with the content.
  • Impact on Traffic Analytics: Understanding unique page views helps in evaluating real audience size and engagement level.
  • Optimization: Focus can be placed on improving pages with low unique views to attract more visitors or increase engagement.
Recognizing the distinction between unique and total page views helps businesses make strategic decisions to enhance user interaction and retention.

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Most popular questions from this chapter

A particularly long traffic light on your morning commute is green \(20 \%\) of the time that you approach it. Assume that each morning represents an independent trial. (a) Over 5 mornings, what is the probability that the light is green on exactly one day? (b) Over 20 mornings, what is the probability that the light is green on exactly four days? (c) Over 20 mornings, what is the probability that the light is green on more than four days?

Printed circuit cards are placed in a functional test after being populated with semiconductor chips. A lot contains 140 cards, and 20 are selected without replacement for functional testing. (a) If 20 cards are defective, what is the probability that at least 1 defective card is in the sample? (b) If 5 cards are defective, what is the probability that at least 1 defective card appears in the sample?

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A shipment of chemicals arrives in 15 totes. Three of the totes are selected at random without replacement for an inspection of purity. If two of the totes do not conform to purity requirements, what is the probability that at least one of the nonconforming totes is selected in the sample?

Four identical computer servers operate a Web site. Only one is used to operate the site; the others are spares that can be activated in case the active server fails. The probability that a request to the Web site generates a failure in the active server is \(0.0001 .\) Assume that each request is an independent trial. What is the mean time until all four computers fail?
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