Answer:
Step-by-step explanation:
For this case we want to find the density function for 
And we have the following density function for the random variable X:

So we can do this replacing 

If we apply square root on both sides we got:

And if we integrate we got this:
![F_Y (y) = [t+ \frac{t^2}{2}] \Big|_{-\sqrt{y}}^0+ [t -\frac{t^2}{2}] \Big|_{0}^{\sqrt{y}}](https://tex.z-dn.net/?f=%20F_Y%20%28y%29%20%3D%20%5Bt%2B%20%5Cfrac%7Bt%5E2%7D%7B2%7D%5D%20%5CBig%7C_%7B-%5Csqrt%7By%7D%7D%5E0%2B%20%5Bt%20-%5Cfrac%7Bt%5E2%7D%7B2%7D%5D%20%5CBig%7C_%7B0%7D%5E%7B%5Csqrt%7By%7D%7D%20)
And replacing we got:
![F_Y (y) = [0 -(-\sqrt{y} +\frac{y}{2})] + [\sqrt{y} -\frac{y}{2}]](https://tex.z-dn.net/?f=%20F_Y%20%28y%29%20%3D%20%5B0%20-%28-%5Csqrt%7By%7D%20%2B%5Cfrac%7By%7D%7B2%7D%29%5D%20%2B%20%5B%5Csqrt%7By%7D%20-%5Cfrac%7By%7D%7B2%7D%5D)

And if we want to find the density function we just need to derivate the pdf like this:
Answer:
D. y²/5² - x²/8² = 1
Step-by-step explanation:
A and B are both incorrectly oriented, and D is the only hyperbola that contains the points (0,5) and (0,-5).
Verification (0,5) and (0,-5) are in the hyperbola:
First replace x and y with corresponding x and y values (We will start with x=0 and y=5)

Then simplify.



If the result is an equation (where both sides are equal to each other) then the original x and y values inputted are valid. The same is true with x and y inputs x=0 and y=-5, or any other point along the hyperbola.
The answer is B. 21 + b = 30
Answer:
9
Step-by-step explanation:
use half the x coefficent and square it
x^2 − 6x + (-3)^2 = 10 + (-3)^2
x^2 - 6x + 9 = 10 + 9
(x - 3)^2 = 19
Answer:
y = 15x
Step-by-step explanation:
A proportional relationship is of the form
y = kx ← k is the constant of proportionality
The only relationship fitting this relationship is
y = 15x with k = 15