Find the value of a

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Concept explainers
Topic Video
Question

Find the value of a

**Text Description:**

The random variable \( x \) has the following continuous probability distribution in the range \( 0 < x < a \), as shown in the figure below.

**Graph Explanation:**

The graph is a two-dimensional plot showing a continuous probability distribution function \( f(x) \) over the interval \( 0 < x < a \).

- The horizontal axis, denoted as \( x \), represents the range of the random variable, extending from \( 0 \) to \( a \).
- The vertical axis, labeled \( f(x) \), represents the probability density function value at each point \( x \).

The function \( f(x) \) is shown as a straight line sloping downward from the point \((0, a)\) on the vertical axis to the point \((a, 0)\) on the horizontal axis, forming a right triangle. This line indicates that the probability density decreases linearly from its maximum value \( a \) at \( x = 0 \) to zero at \( x = a \).
Transcribed Image Text:**Text Description:** The random variable \( x \) has the following continuous probability distribution in the range \( 0 < x < a \), as shown in the figure below. **Graph Explanation:** The graph is a two-dimensional plot showing a continuous probability distribution function \( f(x) \) over the interval \( 0 < x < a \). - The horizontal axis, denoted as \( x \), represents the range of the random variable, extending from \( 0 \) to \( a \). - The vertical axis, labeled \( f(x) \), represents the probability density function value at each point \( x \). The function \( f(x) \) is shown as a straight line sloping downward from the point \((0, a)\) on the vertical axis to the point \((a, 0)\) on the horizontal axis, forming a right triangle. This line indicates that the probability density decreases linearly from its maximum value \( a \) at \( x = 0 \) to zero at \( x = a \).
Expert Solution
Step 1

A function  f:  0,1 is said to be a probability density function if

i.  f(x)0 and

ii. -f(x) dx=1.

Step 2

The given figure shows that as x increases f(x) decreases.

Hence,

 f(x)= a-x,if 0<x<a0otherwise.

 

Now, 0aa-xdx=10ax-adx=-1x-a220a=-10-a22=-1a2=2a=2, since a>0.

steps

Step by step

Solved in 3 steps

Blurred answer
Knowledge Booster
Angles, Arcs, and Chords and Tangents
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
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 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…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
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
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman