Answer:


Step-by-step explanation:
Given

Solving (a):
Find k
To solve for k, we use the definition of joint probability function:

Where

Substitute values for the interval of x and y respectively
So, we have:

Isolate k

Integrate y, leave x:
![k \int\limits^2_{0} y {dx} \, [0,x/2]= 1](https://tex.z-dn.net/?f=k%20%5Cint%5Climits%5E2_%7B0%7D%20y%20%7Bdx%7D%20%5C%2C%20%5B0%2Cx%2F2%5D%3D%201)
Substitute 0 and x/2 for y


Integrate x
![k * \frac{x^2}{2*2} [0,2]= 1](https://tex.z-dn.net/?f=k%20%2A%20%5Cfrac%7Bx%5E2%7D%7B2%2A2%7D%20%5B0%2C2%5D%3D%201)
![k * \frac{x^2}{4} [0,2]= 1](https://tex.z-dn.net/?f=k%20%2A%20%5Cfrac%7Bx%5E2%7D%7B4%7D%20%5B0%2C2%5D%3D%201)
Substitute 0 and 2 for x
![k *[ \frac{2^2}{4} - \frac{0^2}{4} ]= 1](https://tex.z-dn.net/?f=k%20%2A%5B%20%5Cfrac%7B2%5E2%7D%7B4%7D%20-%20%5Cfrac%7B0%5E2%7D%7B4%7D%20%5D%3D%201)
![k *[ \frac{4}{4} - \frac{0}{4} ]= 1](https://tex.z-dn.net/?f=k%20%2A%5B%20%5Cfrac%7B4%7D%7B4%7D%20-%20%5Cfrac%7B0%7D%7B4%7D%20%5D%3D%201)
![k *[ 1-0 ]= 1](https://tex.z-dn.net/?f=k%20%2A%5B%201-0%20%5D%3D%201)
![k *[ 1]= 1](https://tex.z-dn.net/?f=k%20%2A%5B%201%5D%3D%201)

Solving (b): 
We have:

Where 

To find
, we use:

So, we have:



Integrate x leave y
![P(x > 3y) = \int\limits^2_0 x [0,y/3]dy](https://tex.z-dn.net/?f=P%28x%20%3E%203y%29%20%3D%20%5Cint%5Climits%5E2_0%20%20x%20%5B0%2Cy%2F3%5Ddy)
Substitute 0 and y/3 for x
![P(x > 3y) = \int\limits^2_0 [y/3 - 0]dy](https://tex.z-dn.net/?f=P%28x%20%3E%203y%29%20%3D%20%5Cint%5Climits%5E2_0%20%20%5By%2F3%20-%200%5Ddy)

Integrate
![P(x > 3y) = \frac{y^2}{2*3} [0,2]](https://tex.z-dn.net/?f=P%28x%20%3E%203y%29%20%3D%20%5Cfrac%7By%5E2%7D%7B2%2A3%7D%20%5B0%2C2%5D)
![P(x > 3y) = \frac{y^2}{6} [0,2]\\](https://tex.z-dn.net/?f=P%28x%20%3E%203y%29%20%3D%20%5Cfrac%7By%5E2%7D%7B6%7D%20%5B0%2C2%5D%5C%5C)
Substitute 0 and 2 for y




For Samantha, 2 tick marks east is 120 units east because 1 tick is 60 units.
For Ryu, 8 tick marks west is 480 units west because 1 tick is 60 units.
They are walking to form a line. Just add their distances from 0.
120 + 480 = 600.
--------------------------0----------------------------
Ryu: 480 Samantha: 120
480 + 120 = 600.
600 units, or feet.
You can only multiply numbers that are inside the radical symbols