Question

4. Let $f$ be the function of two variables: \begin{equation} f(x, y) = egin{cases} k(2x - y) & \text{if } y < x < 2 \text{ and } x, y > 0\\ 0 & \text{else} \end{cases} \end{equation} (a) Sketch the region where $f > 0$, and find the constant $k$ so that $f$ is a joint probability distribution. (b) Find the probability that $Y > 1$. Sketch the region corresponding to this event. (c) Find the probability that $X + Y > 1$. Sketch the region corresponding to this event.

          4. Let $f$ be the function of two variables:
\begin{equation*}
f(x, y) = egin{cases} k(2x - y) & \text{if } y < x < 2 \text{ and } x, y > 0\\ 0 & \text{else} \end{cases}
\end{equation*}
(a) Sketch the region where $f > 0$, and find the constant $k$ so that $f$ is a joint
probability distribution.
(b) Find the probability that $Y > 1$. Sketch the region corresponding to this event.
(c) Find the probability that $X + Y > 1$. Sketch the region corresponding to this
event.

4. Let f be the function of two variables:

f(x, y) = egincases k(2x - y) if y < x < 2 and x, y > 0
0 else

(a) Sketch the region where f > 0, and find the constant k so that f is a joint
probability distribution.
(b) Find the probability that Y > 1. Sketch the region corresponding to this event.
(c) Find the probability that X + Y > 1. Sketch the region corresponding to this
event.

Added by Timothy G.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Sri K

01/25/2023

Step 1

From the given function, we have f > 0 when 2 - y if y < x < 2 and x, y > 0. This means that the region where f > 0 is the area between the lines y = x and x = 2, in the first quadrant. Show more…

Show all steps

Thanks for your feedback!

4. Let f be the function of two variables k(2-y ify<x<2andx,y>0 0 else (a) Sketch the region where f > 0, and find the constant k so that f is a joint probability distribution. b) Find the probability that Y > 1. Sketch the region corresponding to this event. (c) Find the probability that X + Y > 1. Sketch the region corresponding to this event.