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 right-angled triangle with the hypotenuse as the line segment from point \( (0, a) \) to point \( (a, 0) \).- The horizontal axis is labeled as \( x \).- The vertical axis is labeled as \( f(x) \).- Point \( (0, a) \) represents where the line meets the vertical axis.- Point \( (a, 0) \) represents where the line meets the horizontal axis.- The line indicates a linear decrease from \( f(x) = a \) at \( x = 0 \) to \( f(x) = 0 \) at \( x = a \).Find the value of \( a \). The question asks, "Find the value of \( a \)." Below are the multiple-choice options:- \( \sqrt{3} \)- \( \pm \sqrt{3} \)- \( \sqrt{2} \)- Cannot be determined.- 1- \( \pm \sqrt{2} \)- \( \pm 1 \)The option "Cannot be determined" is selected. There are no graphs or diagrams in the image.

A random variable X is said to follow continuous uniform or rectangular distribution in an interval (a,b0 if its density function is constant over the entire range of the variable X. Its functional form is f(x)= 1b-a if a≤x≤b0 otherwise It is denoted by U(a,b).We know that ∫abf(x)dx=1 , i.e. sum total of all probability in case of continuous distribution is 1. So f(x) = 1a-0; 0≤x≤a0 otherwise ∫0a1adx=1→1ax0a=1→cannot be determined Option (4) is correct

Answered: The random variable x has the following…

Math

Statistics

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

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