Question

Let X ~ Unif[-4, 4], and Y = (X+1)$^2$. (a) Find $f_Y(\frac{9}{4})$ and $f_Y(16)$, where $f_Y(\cdot)$ is the probability density function of Y. Separate your answers with a comma. (b) Find P{Y < 16}.

          Let X ~ Unif[-4, 4], and Y = (X+1)$^2$.
(a) Find $f_Y(\frac{9}{4})$ and $f_Y(16)$, where $f_Y(\cdot)$ is the probability density function of Y.
Separate your answers with a comma.
(b) Find P{Y < 16}.

Let X Unif[-4, 4], and Y = (X+1)^2.
(a) Find fY((9)/(4)) and fY(16), where fY(·) is the probability density function of Y.
Separate your answers with a comma.
(b) Find PY < 16.

Added by Ruben J.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Sheryl Ezze

Step 1

First, let's find the cdf of Y: P(Y ≤ y) = P((X + 1)^2 ≤ y) Taking the square root of both sides (since y is positive): P(|X + 1| ≤ √y) Now, we can split this into two cases: Show more…

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Let X ~ Unif[-4,4], and Y = (X + 1)^2. (a) Find f(r) and f(r = 16), where f(r) is the probability density function of Y. Separate your answers with a comma. (b) Find P(Y < 16).