The proportion of people who respond to a certain mail-order solicitation is a random variable $ X $ having the following density function.\[f(x) =\begin{cases} \frac{2(x+3)}{7}, & 0 < x < 1, \\0, & \text{elsewhere}\end{cases}\]Find the variance of $ X $. **Problem Description:**If a dealer's profit, in units of $3000, on a new automobile can be looked upon as a random variable $X$ having the density function below, find the average profit per automobile.**Density Function:**\[f(x) = \begin{cases} \frac{1}{12}(7 - x), & 0 < x < 2, \\ 0, & \text{elsewhere}\end{cases}\]**Explanation:**This presents a piecewise probability density function (PDF) $f(x)$ defined for a random variable $X$. The function is defined as:- $\frac{1}{12}(7 - x)$ for $0 < x < 2$: This indicates that within the range of 0 to 2, the density function follows a linear decrease as a function of $x$.- 0 elsewhere: Outside the range of 0 to 2, the probability density function is zero, meaning there is no chance of the profit value falling outside this interval.

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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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The probability density function of a discrete random variable X is given by the following table: Px(X = 0) = .54 Px(X = 1) = .16 Px(X = 2) = .06 Px(X = 3) = .04 Px(X = 4) = .20 %3D i) Compute E(X). ii) Compute Var(X).
Answer the following question:
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The proportion of people who respond to a certain mail-order solicitation is a random variable X having the following density function. f(x) = 2(x+3) 7 O " 0