a) Find the probability that the friend is between 5 and 25 minutes late b) it is 10 AM. There is a 30% probability the friend will arrive within how many minutes? a) The probability that the friend is between 5 and 25 minutes late is Type an integer or a decimal Round to three decimal places as needed) b) There is a 30% probability the friend will arrive within minutes. Type a whole number) 1 man 8 1/30- 10 20 30X Time 060
a) Find the probability that the friend is between 5 and 25 minutes late b) it is 10 AM. There is a 30% probability the friend will arrive within how many minutes? a) The probability that the friend is between 5 and 25 minutes late is Type an integer or a decimal Round to three decimal places as needed) b) There is a 30% probability the friend will arrive within minutes. Type a whole number) 1 man 8 1/30- 10 20 30X Time 060
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![**Understanding Uniform Probability Density Functions**
In this exercise, we'll explore the concept of a uniformly distributed random variable representing the lateness of a friend. We're given that the uniformly distributed variable \( X \) represents the lateness of this friend in minutes.
**(a) Calculating Probability Between Specific Intervals**
1. **Question (a):** Find the probability that the friend is between 5 and 25 minutes late.
- **Input:** (Type an integer or a decimal. Round to three decimal places as needed.)
**(b) Finding the Time Interval for a Given Probability**
2. **Question (b):** It is 10 A.M. There is a 30% probability the friend will arrive within how many minutes?
- **Input:** (Type a whole number.)
**Detailed Explanation of the Graph**
The graph depicted on the right is a uniform probability density function (PDF). The density function delineates a constant probability over a specified interval, indicating that an event is equally likely to occur at any point within this interval.
- **The x-axis:** Represents time (in minutes).
- **The y-axis:** Represents the density value.
- **Range on x-axis:** The interval is between 0 and 30 minutes.
- **Density value (y-axis):** Remains constant across the defined interval.
- For a uniform distribution \(X \sim U(a, b)\), the probability density function \(f(x)\) is defined as:
\[
f(x) = \frac{1}{b - a} \quad \text{for} \quad a \leq x \leq b
\]
- In this case, \(a = 0\) and \(b = 30\), hence the density value \(f(x) = \frac{1}{30 - 0} = \frac{1}{30}\).
- The graph displays a horizontal line at \(y = \frac{1}{30}\), from \(x = 0\) to \(x = 30\).
By working through these steps, students will learn to compute probabilities for uniform distributions and understand using probability density functions for practical time-related predictions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffeeb79a1-23ea-4f54-b610-a8910f30c066%2Fc3167926-a3b4-435f-b687-943c930b6edb%2Fjs7kji6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Understanding Uniform Probability Density Functions**
In this exercise, we'll explore the concept of a uniformly distributed random variable representing the lateness of a friend. We're given that the uniformly distributed variable \( X \) represents the lateness of this friend in minutes.
**(a) Calculating Probability Between Specific Intervals**
1. **Question (a):** Find the probability that the friend is between 5 and 25 minutes late.
- **Input:** (Type an integer or a decimal. Round to three decimal places as needed.)
**(b) Finding the Time Interval for a Given Probability**
2. **Question (b):** It is 10 A.M. There is a 30% probability the friend will arrive within how many minutes?
- **Input:** (Type a whole number.)
**Detailed Explanation of the Graph**
The graph depicted on the right is a uniform probability density function (PDF). The density function delineates a constant probability over a specified interval, indicating that an event is equally likely to occur at any point within this interval.
- **The x-axis:** Represents time (in minutes).
- **The y-axis:** Represents the density value.
- **Range on x-axis:** The interval is between 0 and 30 minutes.
- **Density value (y-axis):** Remains constant across the defined interval.
- For a uniform distribution \(X \sim U(a, b)\), the probability density function \(f(x)\) is defined as:
\[
f(x) = \frac{1}{b - a} \quad \text{for} \quad a \leq x \leq b
\]
- In this case, \(a = 0\) and \(b = 30\), hence the density value \(f(x) = \frac{1}{30 - 0} = \frac{1}{30}\).
- The graph displays a horizontal line at \(y = \frac{1}{30}\), from \(x = 0\) to \(x = 30\).
By working through these steps, students will learn to compute probabilities for uniform distributions and understand using probability density functions for practical time-related predictions.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 1 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman