A few days ago
frostwizrd

Statistics: Conditional probability. Any help please?

This isn’t a homework question; I have a final in my statistics class tomorrow, and I need to understand conditional probability. 🙁

Let X and Y be independent and have the same geometric distribution with success probability p.

Find the conditional distribution of X given X + Y = n.

The book doesn’t seem to give a good explanation of this, so any help would be great! Thanks!

A few days ago
Anonymous

Wish I could help but you lost me on ‘X’.
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A few days ago
Anonymous
I’m not entirely sure about it, but this is my gut reaction to this kind of question:

If X and Y have the same probability of success and they’ve got the same geometric distribution (not entirely sure of that, but i’m pretty sure it means that they’re got the same +/- value, which i can explain later) then that means the probabilities are both p.

If n is the value of the sum of the probabilities, it may mean that n = 2p because the probabilities are the same. But you have to make sure you know what the geometric distribution is around that probability.

I’m not sure what the geom. distribution is, but look here:

http://en.wikipedia.org/wiki/Geometric_distribution

for an explanation.

In reading the description, it means basically one of two things:

1. how many trials it takes to get a success

or

2. how many trials it takes to get a failure.

Notice that in the wiki page it describes both. You can use and describe both or one of these as long as you’re CONSISTENT in your explanation.

i.e. if you say on the test that the geometric distribution describes how many successes, ALWAYS stick with the probabilities and formulas that will give you successes.

Anyway, conditional probability is basically the success (or failure) outcomes of random trials. I.e. flipping a coin.

Say the prob. of getting heads on a coin is 0.25 (25%, 1/4 whatever), and we’ll call this the SUCCESS, and this is probability P. This means the prob of FAILING is 1-P, which is 1-0.25 or 0.75 (75%, whatever). Know what i mean? So if you keep talking about the success, stick with the success.

Back to your problem, and holy crap this is a long answer, i am not entirely sure. sorry.

Good luck on your final. That’s tough stuff!

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A few days ago
David C
The answer is 1/(n-1) for i
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5 years ago
?
P (B & ^A) = P (B) – P (B&A) = .6 – .3 = .3
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