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  2. Joint probability distribution - Wikipedia

    en.wikipedia.org/wiki/Joint_probability_distribution

    If the points in the joint probability distribution of X and Y that receive positive probability tend to fall along a line of positive (or negative) slope, ρ XY is near +1 (or −1). If ρ XY equals +1 or −1, it can be shown that the points in the joint probability distribution that receive positive probability fall exactly along a straight ...

  3. Distribution of the product of two random variables - Wikipedia

    en.wikipedia.org/wiki/Distribution_of_the...

    The joint pdf () exists in the -plane and an arc of constant value is shown as the shaded line. To find the marginal probability f Z ( z ) {\displaystyle f_{Z}(z)} on this arc, integrate over increments of area d x d y f ( x , y ) {\displaystyle dx\,dy\;f(x,y)} on this contour.

  4. Multivariate normal distribution - Wikipedia

    en.wikipedia.org/wiki/Multivariate_normal...

    Hoyt distribution, the pdf of the vector length of a bivariate normally distributed vector (correlated and centered) Complex normal distribution , an application of bivariate normal distribution Copula , for the definition of the Gaussian or normal copula model.

  5. Likelihood function - Wikipedia

    en.wikipedia.org/wiki/Likelihood_function

    More generally, for each value of , we can calculate the corresponding likelihood. The result of such calculations is displayed in Figure 1. The result of such calculations is displayed in Figure 1. The integral of L {\textstyle {\mathcal {L}}} over [0, 1] is 1/3; likelihoods need not integrate or sum to one over the parameter space.

  6. Joint entropy - Wikipedia

    en.wikipedia.org/wiki/Joint_entropy

    The joint entropy of a set of variables is less than or equal to the sum of the individual entropies of the variables in the set. This is an example of subadditivity . This inequality is an equality if and only if X {\displaystyle X} and Y {\displaystyle Y} are statistically independent .

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