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(2) (20 pts) Suppose we want to construct a continuous joint density function of the form fx.y(x,y) = c(x3 + 3x2y + 3xy® + y*), where c is some constant, and the variables X and Y are restricted to the real interval [0,1]. a) (2 pts) How can you tell, just by looking at this pdf, that Xand Y are dependent? b) (4 pts) What is the correct valuc of the constant e c 4 pts) What are the marginal distributions of X and Y? d) (4 pts) What are the expected values of X and ? e) (4 pts) What is the covariance between Xand Y? f) (2 pts) Does the answer to part e) also prove that X and Y are dependent?
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