/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 184 Decide whether a discrete or con... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 184

Decide whether a discrete or continuous random variable is the best model for each of the following variables: (a) The time for a computer algorithm to assign an image to a category. (b) The number of bytes used to store a file in a computer. (c) The ozone concentration in micrograms per cubic meter. (d) The ejection fraction (volumetric fraction of blood pumped from a heart ventricle with each beat). (e) The fluid flow rate in liters per minute.

Short Answer

Expert verified
(a) Continuous, (b) Discrete, (c) Continuous, (d) Continuous, (e) Continuous.

Step by step solution

01

Analyze Time for Algorithm

The time for a computer algorithm to assign an image to a category can be any real number, depending on various factors like system speed and image complexity. Therefore, it can take any value on the continuous number line over some interval. Hence, it's a continuous random variable.
02

Analyze Number of Bytes

Bytes are counted in whole numbers since you cannot have a fraction of a byte in standard memory representation. Therefore, the number of bytes is a distinct, countable quantity. Thus, it's a discrete random variable.
03

Analyze Ozone Concentration

The ozone concentration is measured in micrograms per cubic meter, which can take any non-negative real value. It can be infinitely precise, depending on the measurement tool used. As such, it's considered a continuous random variable.
04

Analyze Ejection Fraction

Although the ejection fraction is a percentage, it can vary continuously from 0 to 100 without being restricted to discrete steps. This makes the ejection fraction a continuous random variable.
05

Analyze Fluid Flow Rate

Like ozone concentration, the fluid flow rate measured in liters per minute can take any real value, continuously, depending on the device and measurement precision. Therefore, it is a continuous random variable.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Discrete Random Variables
Discrete random variables are fascinating elements in the realm of probability and statistics. They are used to represent countable phenomena, meaning their possible values can be counted, often as whole numbers. For instance, consider the number of bytes used to store a file in a computer. You can't store half a byte; hence, the values here are distinct and separate, making them countable.
  • Discrete variables often arise in scenarios where the variable is a result of counting something, like the number of books on a shelf or the number of people in a room.
  • These variables generally take on integer values.
  • Common distributions for discrete random variables include the Poisson and Binomial distributions.
Understanding discrete random variables helps in statistical modeling, as they allow for predictions and distributions that align with countable outcomes.
Continuous Random Variables
Continuous random variables are vital for modeling a variety of real-world situations where the possible outcomes are not countable but lie on a continuum of values. These variables can take any value within a given range, such as the time it takes for a computer algorithm to categorize an image.
  • Continuous variables come into play when measuring time, distance, temperature, and other phenomena requiring precision. For example, the algorithm time can be any real number, determined by several continuous factors.
  • Commonly associated with distributions like the Normal, Exponential, and Uniform distributions.
  • They require careful consideration when measuring instruments can influence precision.
Grasping continuous random variables is fundamental to statistical analysis, allowing engineers to measure and model data that falls along a spectrum.
Statistical Modeling
Statistical modeling is a powerful tool engineers use to predict and make sense of data, utilizing frameworks like discrete and continuous random variables. This process involves creating mathematical models to represent real-world processes and interpret various data patterns.
  • Models are built on assumptions of probability and the underlying randomness of data.
  • They require an understanding of both discrete and continuous data to ensure flexibility and accuracy.
  • Correct statistical modeling can lead to improved resource planning, decision-making, and innovation.
In probability for engineers, statistical modeling underpins many analyses, ensuring engineers can tackle complex problems with refined strategies.
Random Variable Analysis
Random variable analysis is a technique used to understand the behavior and properties of random variables within a statistical framework. This involves the examination of both discrete and continuous types of random variables.
  • It's crucial for determining how variables like ozone concentration or ejection fraction distribute across a set of potential outcomes.
  • Analyzing these provides insights into expected values, variances, and other essential properties of variables.
  • Through effective analysis, engineers can forecast outcomes and establish probabilistic models that are robust and reliable.
Random variable analysis is indispensable in understanding data patterns and variability, empowering engineers to manage uncertainties and design resilient systems.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A lot contains 15 castings from a local supplier and 25 castings from a supplier in the next state. Two castings are selected randomly, without replacement, from the lot of \(40 .\) Let \(A\) be the event that the first casting selected is from the local supplier, and let \(B\) denote the event that the second casting is selected from the local supplier. Determine: (a) \(P(A)\) (b) \(P(B \mid A)\) (c) \(P(A \cap B)\) (d) \(P(A \cup B)\) Suppose that 3 castings are selected at random, without replacement, from the lot of \(40 .\) In addition to the definitions of events \(A\) and \(B,\) let \(C\) denote the event that the third casting selected is from the local supplier. Determine: (e) \(P(A \cap B \cap C)\) (f) \(P\left(A \cap B \cap C^{\prime}\right)\)

A byte is a sequence of eight bits and each bit is either 0 or 1 . (a) How many different bytes are possible? (b) If the first bit of a byte is a parity check, that is, the first byte is determined from the other seven bits, how many different bytes are possible?

Four bits are transmitted over a digital communications channel. Each bit is either distorted or received without distortion. Let \(A i\) denote the event that the ith bit is distorted, \(i=1, \ldots .4\) (a) Describe the sample space for this experiment. (b) Are the \(A\) 's mutually exclusive? Describe the outcomes in each of the following events: (c) \(A_{1}\) (d) \(A_{1}^{\prime}\) (e) \(A_{1} \cap A_{2} \cap A_{3} \cap A_{4}\) (f) \(\left(A_{1} \cap A_{2}\right) \cup\left(A_{3} \cap A_{4}\right)\)

A robotic insertion tool contains 10 primary components. The probability that any component fails during the warranty period is 0.01 . Assume that the components fail independently and that the tool fails if any component fails. What is the probability that the tool fails during the warranty period?

A steel plate contains 20 bolts. Assume that 5 bolts are not torqued to the proper limit. 4 bolts are selected at random, without replacement, to be checked for torque. (a) What is the probability that all 4 of the selected bolts are torqued to the proper limit? (b) What is the probability that at least 1 of the selected bolts is not torqued to the proper limit?
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.