Suppose a random variable X has a probability density function in img.jpg. a. Find the value of k that makes this a probability density function.b. Find P(0.4≤X≤1).c. Find P(X≤0.4|X≤0.8)d. Find F(b) = P(X≤b) and sketch the graph of this function. **Mathematical Function Description:**The function \( f(x) \) is defined as follows:- For values of \( x \) in the range \( 0 \leq x \leq 1 \), the function is given by: \[ f(x) = kx(1 - x) \]- For values of \( x \) outside this range (i.e., elsewhere), the function is defined as: \[ f(x) = 0 \]**Explanation:**- This is a piecewise function where the behavior of \( f(x) \) changes depending on the value of \( x \).- Within the interval from 0 to 1, \( f(x) \) is a quadratic expression that depends on the parameter \( k \).- Outside the interval from 0 to 1, the function has a constant value of 0.This setup is often used in mathematical contexts where the function is only relevant or has meaningful values within a certain range.

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Suppose a random variable X has a probability density function in img.jpg. a. Find the value of k that makes this a probability density function. b. Find P(0.4≤X≤1). c. Find P(X≤0.4|X≤0.8) d. Find F(b) = P(X≤b) and sketch the graph of this function.

Suppose a random variable X has a probability density function in img.jpg. a. Find the value of k that makes this a probability density function. b. Find P(0.4≤X≤1). c. Find P(X≤0.4|X≤0.8) d. Find F(b) = P(X≤b) and sketch the graph of this function.

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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