Question

The proportion of people who respond to a certain mail-order solicitation is a random variable $X$ having the following density function. $$ f(x) = \begin{cases} \frac{2(x+2)}{5}, & 0 < x < 1 \\ 0, & \text{elsewhere} \end{cases} $$ Find $\sigma^2_{g(X)}$ for the function $g(X) = 3X^2 + 5$.

Name: the proportion of people who respond to a certain mail order solicitation is a random variable x having the following density function fx begincases frac2x25 0 x 1 0 textelsewhere endcases f 03776
Uploaded: 2022-03-27T12:06:33-08:00
Duration: 3 min 30 s
Channel: Ekaveera Kumar
Description: the proportion of people who respond to a certain mail order solicitation is a random variable x having the following density function fx begincases frac2x25 0 x 1 0 textelsewhere endcases f 03776

          The proportion of people who respond to a certain mail-order solicitation is a random variable $X$ having the following density function.
$$
f(x) = \begin{cases}
\frac{2(x+2)}{5}, & 0 < x < 1 \\
0, & \text{elsewhere}
\end{cases}
$$
Find $\sigma^2_{g(X)}$ for the function $g(X) = 3X^2 + 5$.

$the proportion of people who respond to a certain mail order solicitation is a random variable x having the following density function fx begincases frac2x25 0 x 1 0 textelsewhere endcases f 03776$

Added by Krystal W.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Ekaveera Kumar

03/27/2022

Step 1

$$ E(X) = \int_0^1 x \cdot \frac{2(x+2)}{5} dx = \frac{2}{5} \int_0^1 (x^2 + 2x) dx = \frac{2}{5} \left[ \frac{x^3}{3} + x^2 \right]_0^1 = \frac{2}{5} \left( \frac{1}{3} + 1 \right) = \frac{2}{5} \cdot \frac{4}{3} = \frac{8}{15} $$ Show more…

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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. $$ f(x) = \begin{cases} \frac{2(x+2)}{5}, & 0 < x < 1 \\ 0, & \text{elsewhere} \end{cases} $$ Find $\sigma^2_{g(X)}$ for the function $g(X) = 3X^2 + 5$.