OpenStudy (tiffany_rhodes):

Let B and C be independent random variables both having the pdf: f(x) = cx^2 if 1

OpenStudy (freckles):

Sounds like we need to find c first

3 years ago
OpenStudy (tiffany_rhodes):

yeah, that's what I thought but I'm not quite sure how to go about doing that.

3 years ago
OpenStudy (freckles):

i think you need to find c such that We need \[\int\limits_{1}^{3}cx^2 dx=1\]

3 years ago
OpenStudy (tiffany_rhodes):

c = 3/26?

3 years ago
OpenStudy (freckles):

yes sounds good

3 years ago
OpenStudy (freckles):

Thinking about that last question.... Thoughts pending...

3 years ago
OpenStudy (freckles):

So I know that quadratics have two real roots if \[B^2-4AC>0\]

3 years ago
OpenStudy (freckles):

And A=1 here so we have

3 years ago
OpenStudy (tiffany_rhodes):

lol alright. Oh and why did we set the integral equal to 1?

3 years ago
OpenStudy (freckles):

\[B^2-4C>0\]

3 years ago
OpenStudy (freckles):

just like in a discrete pdf the sum of the probabilities must add up to be 1

3 years ago
OpenStudy (tiffany_rhodes):

oh, okay. That makes sense.

3 years ago
OpenStudy (freckles):

@SithsAndGiggles if you want you can look at this last question she has My thoughts are pending slow on it

3 years ago
OpenStudy (tiffany_rhodes):

Alright. I don't know if it will help but my hw says the answer is .12

3 years ago
OpenStudy (anonymous):

\[P(B^2-4C>0)=P(B^2>4C)=P(|B|>2\sqrt C)\] At least two nice ways to find this sort of probability: method of distribution functions, or method of transformations. Do either of these sound familiar? (Method of moment-generating functions might also work, but that sounds brutal.)

3 years ago
OpenStudy (tiffany_rhodes):

The first two aren't familiar whatsoever and the moment-generating functions was discussed very briefly in my lecture.

3 years ago
OpenStudy (tiffany_rhodes):

were*

3 years ago
OpenStudy (freckles):

https://engineering.purdue.edu/~ipollak/ee302/SPRING04/exams/ex2_sol.pdf This pdf has a similar problem see problem 5

3 years ago
OpenStudy (anonymous):

Try finding the distribution of the rv function \(B^2-4C\) using the method of distribution functions.

3 years ago
OpenStudy (tiffany_rhodes):

we haven't covered that.

3 years ago
OpenStudy (anonymous):

Sorry, I meant the MGF method, not CDF >.<

3 years ago
OpenStudy (anonymous):

Hmm that method might not be very useful here... What else do you know to do with functions of random variables?

3 years ago
OpenStudy (tiffany_rhodes):

I have to go to class and I'll ask my TA. Thank you both for trying.

3 years ago
OpenStudy (anonymous):

For what it's worth, you're welcome. There might be some trick to it we're not seeing. Notice that \(\dfrac{3}{26}\approx.12\), that might be a clue.

3 years ago