Suppose that f(x) = 1.5x² for −1 < x < 1. Determine the following probabilities: a) P(0 < X) = 0.5 b) P(0.8 < X) = i 0.499 (Round the answer to 3 decimal places.) c) P(-0.5 ≤ x ≤ 0.5) = 0.125 (Round the answer to 3 decimal places.)
Suppose that f(x) = 1.5x² for −1 < x < 1. Determine the following probabilities: a) P(0 < X) = 0.5 b) P(0.8 < X) = i 0.499 (Round the answer to 3 decimal places.) c) P(-0.5 ≤ x ≤ 0.5) = 0.125 (Round the answer to 3 decimal places.)
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
16) Solve with the complete method. Please solve part (b) only.
b) P(0.8<X)=
![### Probability Distributions and Calculations
**Problem Statement:**
Suppose that \( f(x) = 1.5x^2 \) for \( -1 < x < 1 \). Determine the following probabilities:
1. Calculate \( P(0 < X) \):
- \[ P(0 < X) = 0.5 \]
2. Calculate \( P(0.8 < X) \):
- \[ \boxed{0.499} \]
- (Round the answer to 3 decimal places)
3. Calculate \( P(-0.5 \leq X \leq 0.5) \):
- \[ P(-0.5 \leq X \leq 0.5) = 0.125 \]
- (Round the answer to 3 decimal places)
4. Calculate \( P(X < -2) \):
- \[ P(X < -2) = 0 \]
5. Calculate \( P(X < 0 \text{ or } X > 0.5) \):
- \[ P(X < 0 \text{ or } X > 0.5) = 1 \]
6. Determine \( x \) such that \( P(x < X) = 0.05 \):
- \[ x = 0.966 \]
- (Round the answer to 3 decimal places)
**Explanation of Diagram (if any):**
The image contains textual representations of probabilities and their calculated values in boxes. There are no graphical representations or diagrams present in this image that require explanation.
**Note on Context and Calculation:**
These are probability calculations based on the given probability density function \( f(x) = 1.5x^2 \). Each subproblem requires integrating the function over specific intervals or determining certain values that satisfy given conditions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7824f8d0-65fb-442c-84f7-7ea5547717e1%2F8da969b9-17fa-4fc9-b687-1c7f6ac0ca50%2F6ar08lt_processed.png&w=3840&q=75)
Transcribed Image Text:### Probability Distributions and Calculations
**Problem Statement:**
Suppose that \( f(x) = 1.5x^2 \) for \( -1 < x < 1 \). Determine the following probabilities:
1. Calculate \( P(0 < X) \):
- \[ P(0 < X) = 0.5 \]
2. Calculate \( P(0.8 < X) \):
- \[ \boxed{0.499} \]
- (Round the answer to 3 decimal places)
3. Calculate \( P(-0.5 \leq X \leq 0.5) \):
- \[ P(-0.5 \leq X \leq 0.5) = 0.125 \]
- (Round the answer to 3 decimal places)
4. Calculate \( P(X < -2) \):
- \[ P(X < -2) = 0 \]
5. Calculate \( P(X < 0 \text{ or } X > 0.5) \):
- \[ P(X < 0 \text{ or } X > 0.5) = 1 \]
6. Determine \( x \) such that \( P(x < X) = 0.05 \):
- \[ x = 0.966 \]
- (Round the answer to 3 decimal places)
**Explanation of Diagram (if any):**
The image contains textual representations of probabilities and their calculated values in boxes. There are no graphical representations or diagrams present in this image that require explanation.
**Note on Context and Calculation:**
These are probability calculations based on the given probability density function \( f(x) = 1.5x^2 \). Each subproblem requires integrating the function over specific intervals or determining certain values that satisfy given conditions.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps
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