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# 6. The joint density of the random variables X and Y is given as f(x,y) C-...

## Question

###### 6. The joint density of the random variables X and Y is given as f(x,y) C-...

6. The joint density of the random variables X and Y is given as f(x,y) C- 'y21 otherwise i) Find c such that f(x, y) is a valid density function. (8 pts) ii) Set up the calculation for P(X < 2, Y > 2). You do not need to compute this value. (5 pts) iii) Find the marginal distribution of X and the marginal distribution of Y. (14 pts) iv) Find E(X) and E(Y)(10 pts) v) Find og and oſ (12 pts) vi) Find o xy (10 pts) vii) Find pxy. (4 pts) viii) Sketch a plot like the one below (assume the axes increase from down to up and left to right), add points that might produce such a p value. (2 pts)

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