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December 5th, 2010, 01:48 PM   #1
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Joint Probability

Say for example the Probability P(A|B) =1/4. The joint probability of this would be P(A|B)P(B). However, you are not given the probability of B. How would you go ahead and do this?
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December 5th, 2010, 04:27 PM   #2
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Re: Joint Probability

Try to state the problem precisely. I can't tell what you are looking for.
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December 6th, 2010, 04:52 AM   #3
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Re: Joint Probability

OK. Here is the problem.

The random variables X and Y are discreet distributed with the values 1,2,3,4 and 0,1,2,3. Y is B(3, 0.5)-distributed. Given below is the table for the conditional probabilities P(X = i|Y = k) for i = 1,2,3, 4 and k = 0,1,2,3:

Calculate P(X = i, Y = k) for i = 1, . . . , 4 and k = 0, . . . , 3.

My understanding is that this is a joint probability. From the join probability formula, we have: P(X = i, Y = k)P(Y = k). We already have (X = i, Y = k) in the table but I don't know how I will get P(Y=K)

Thanks in advance.
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December 6th, 2010, 12:57 PM   #4
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Re: Joint Probability

Quote:
Y is B(3, 0.5)-distributed
I don't know what this means, but it should tell you what P(Y=k) is.
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December 6th, 2010, 01:24 PM   #5
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Re: Joint Probability

I think it means it is binomially distributed.
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December 7th, 2010, 01:00 PM   #6
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Re: Joint Probability

I'll assume it means binomial with n=3 and p=0.5. In that case P(k=0)=P(k=3)=1/8 and P(k=1)=P(k=2)=3/8.
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