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the-probability-density-function-with-two-continous-random-variable-X-and-Y-is-a-follows-f-x-y-0-x-other-2x-2y-0-lt-x-lt-1-0-lt-y-lt-1-determine-the-correlation-coeffic




Question Number 145674 by syamilkamil1 last updated on 07/Jul/21
the probability density function with two continous random  variable X and Y is a follows :    f(x,y) = {_(0  , x other) ^(2x + 2y  , 0 < x < 1, 0 < y < 1)     determine the correlation coefficient  between X and Y!
$${the}\:{probability}\:{density}\:{function}\:{with}\:{two}\:{continous}\:{random} \\ $$$${variable}\:{X}\:{and}\:{Y}\:{is}\:{a}\:{follows}\:: \\ $$$$ \\ $$$${f}\left({x},{y}\right)\:=\:\left\{_{\mathrm{0}\:\:,\:{x}\:{other}} ^{\mathrm{2}{x}\:+\:\mathrm{2}{y}\:\:,\:\mathrm{0}\:<\:{x}\:<\:\mathrm{1},\:\mathrm{0}\:<\:{y}\:<\:\mathrm{1}} \right. \\ $$$$ \\ $$$${determine}\:{the}\:{correlation}\:{coefficient} \\ $$$${between}\:{X}\:{and}\:{Y}! \\ $$

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