Calculate the correlation coefficient ρ of a two-dimensional discrete random vector (<i>X</i>, <i>Y</i>) with only a finite number of values, and the <i> obtained for the correlation coefficient ρ Mathematical expectations of X</i> and <i>Y</i>E(<i>X</i>),E(<i>Y</i>)，variance is D(<i>X</i>),D(<i>Y</i>)，标准差σ_<i>X</i>,σ<sub><i>Y</i></su

In the input box below, enter three sets of data separated by two "|" characters. Each real number of each set of data is separated by a comma. These real numbers can be entered as fractions, for example, 2/3 represents three points. Second, you can also enter in decimal form.

The first set of data is all possible values for <i>X</i> is <i>x</i>₁,<i>x</i>₂,...,<i>x_n</i>，The second set of data is <i>Y</i> all possible values are <i>y</i>₁,<i>y</i>₂,...,<i>y_m</i>，The third set of data is (<i>X</i>,<i>Y</i>) probability of all possible pairs of values <i>p</i>₁₁,<i>p</i>₁₂,...,<i>p</i>_1<i>n</i>, <i>p</i>₂₁,<i>p</i>₂₂,...,<i>p</i>_2<i>n</i>,...<i>p_m</i>₁,<i>p_m</i>₂,...,<i>p_mn</i>。

Click the "Start Calculation" button after entering the data and you will get the desired calculation result.