Jointly distributed random variables
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چکیده
Similarly we can get the distribution function of Y easily from the joint distribution function of X and Y : FY (y) = lim x→∞ (x, y) = F (∞, y). The distribution functions FX and FY are sometimes called the marginal distribution functions of X and Y respectively. The joint distribution function F of X and Y contains all the statistical information about X and Y . In particular, given the joint distribution function F of X and Y , we can calculate the probability of any event defined in terms of X and Y . For instance, for any real numbers a ≤ b and c ≤ d, we have P(a < X ≤ b, c < Y ≤ d) = F (b, d)− F (a, d)− F (b, c) + F (a, c).
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