The consumption of two types of household goods (X and Y) follows a hypothetical joint probability density

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The consumption of two types of household goods (X and Y) follows a hypothetical joint probability density function as follows:

fXY (x, y) = c(x + y ) < x < < y < 2 2 for 0 1 and 0 1 where x and y are normalized to the respective maximum value for all the houses. Determine the constant c such that fxy(x,y) is a legitimate joint density function. Evaluate the marginal density functions fX(x) and fY(y). Evaluate the probability that 0 < x < 0.5 and 0 < y < 0.25 . Are the random variables statistically uncorrelated? Why?

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