# Let P(X=3)=0.4 and P(Y=2)=0.5. Find P(X=3,Y=2).

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. – Cristian Oct 9 '12 at 17:17
The answer can be anything between 0.4 and zero if independence is not assumed. – Harald Hanche-Olsen Oct 9 '12 at 17:18
I checked, and they are not independent. – jrquick Oct 9 '12 at 17:20
@JeremyQuick: How do they depend on each other? – Thomas Oct 9 '12 at 17:26
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. – Cristian Oct 9 '12 at 17:26