A dart is thrown at a board with radius 7. the point the dart hits is uniformly distributed on the cricular board. Find the expected distance of the point from center of board. The answer uses the survival function but I do not how exactly. I am not a mathematician and need help. I just like math thats all. It says s(t)= T>t= Pr (X^2 +Y^2 > t^2) = area of circle with r=7-area pfcircle with r=t/ area of circle with r=7. I am lost ......
are you using a manual to prepare for P? I highly recommend you do so! Googling is just not enough sometimes :P
To put the definition in english though... I would say it's easy to think of the survival function S[X] is the equivalent of saying the probability that something survives for X length of time, which is to say that it "dies" after X length of time. So you may think of it as P[X>x] which is the converse of F[x] which says something "dies" before x or P[X<x]
The relationship between S[X], F[X], and f[X] is something that you definitely need to be aware of for this exam. Hope that helped!!
Thank you Sir.... I am not sure what your name is but I appreciate the info. I just do not get what the equation means in this problem like how does T >t = that equation with the areas. I failed P 3 times with my highest score at 5. I practice a little here and there thinking I might learn a little a more. I am now using Dr. Ostaszewski's manual.
No answers? How does the distance formula fit with the T in the survival?
Well.... you can consider the length from the origin a joint pdf yes? You can expect a Y and expect an X. And depending on those X and Y you'll calculate your expected distance from the origin. (pythagorus here!)
But I think the easy solution here would be to recognize this is a uniform distribution... What can you draw from that? You can come up with you p(x) your F(x) and your S(x).
It's easy to calculate E[x] from any of those bits of information. In this problem they utilized S[x] and the identity that Integral from 0 to Inf of S[x] equal E[x]. But since this is a uniform distribution it cuts out all the calculus. Your S[x] is just area of hitting the board between x and 7 out of the area of the whole board. (we are using areas because it is a uniform distribution and it's easier than integrating joint distribution here) To put it in steps I would say this.....
You should get 4 and 2/3. Is this correct?
I feel like this is still confusing so I'm hoping someone else can come in and save the day :lol:
Thanks again.... I think I get it now....... You can figure out what F(X) is, just the (area of circle with r=x)/(area of circle with r=7), then 1-F(x) would = S (X), then you could finally integrate that function from 0 to 7 to get the answer. Thanks...... I think thats right? What your name, maybe we can study sometime if your from NY.