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Let $P(X=3)=0.4$ and $P(Y=2)=0.5$. I need to find $P(X=3,Y=2)$.

I'm thinking that I ought to just multiply the two probabilities: $P(X=3) \times P(Y=2)$ to get $0.4 \times 0.5 = 0.2$, but is this correct?

If not, how do I go about finding this? There is a chance that it is uncomputable.

Edit: They are not independent.

Both X and Y are random variables.

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    If you assume that X and Y are independent random variables, then your answer is correct. Otherwise, we would need a bit more information to answer your question.2012-10-09
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    The answer can be anything between 0.4 and zero if independence is not assumed.2012-10-09
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    I checked, and they are not independent.2012-10-09
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    @JeremyQuick: How do they depend on each other?2012-10-09
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    For instance, do you know the likelihood of Y given X. If so, you could compute $P(X \cap Y)=P(Y|X)P(X)$. But without any further information, it is difficult to recover the joint probability from the marginals.2012-10-09
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    I edited the question with additional information, such as X and Y are random variables and there may be no computable answer.2012-10-09

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If you assume that X and Y are independent random variables, then your answer is correct. Otherwise, we would need a bit more information to answer your question.