Question

Problem 7. Let X ~uniform [-3,3], and suppose Y = g(X), where \begin{equation} g(x) = \begin{cases} 2 & , -1 \le x \le 1 \\ 2/x^2 & , 1 < |x| \le 2 \\ 0 & , \text{otherwise} \end{cases} \end{equation} Find $f_Y(y)$ for $-\infty < y < \infty$.

          Problem 7.
Let X ~uniform [-3,3], and suppose Y = g(X), where
\begin{equation*}
g(x) = \begin{cases}
2 & , -1 \le x \le 1 \\
2/x^2 & , 1 < |x| \le 2 \\
0 & , \text{otherwise}
\end{cases}
\end{equation*}
Find $f_Y(y)$ for $-\infty < y < \infty$.

Problem 7.
Let X uniform [-3,3], and suppose Y = g(X), where

g(x) =
2 , -1 ≤ x ≤ 1

2/x^2 , 1 < |x| ≤ 2

0 , otherwise

Find fY(y) for -∞ < y < ∞.

Added by Seth B.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Avinash Vishwakarma

06/05/2022

Step 1

Step 1: To find the probability density function of Y, we need to consider the different intervals of X that map to Y under the function g(x). Show more…

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Problem 7. Let X ~ uniform [-3,3], and suppose Y = g(X), where g(x) = {2, -1 <= x <= 1, 2/x^2, 1 < |x| <= 2, 0, otherwise} Find f_Y(y) for -∞ < y < ∞.