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# Question 1 (10 marks)Let the two random variables X and Y have the following joint probability density function (pdf)k + y; if 0 < I < 2,2 < y < 1 fx(â...

## Question

###### Question 1 (10 marks)Let the two random variables X and Y have the following joint probability density function (pdf)k + y; if 0 < I < 2,2 < y < 1 fx(â‚¬,y) = 0; otherwiseDraw diagram of the joint sample space of X and Y.markb) Show that k2marks)Find the marginal probability density functions fx (1) and fy (y).2 marks)Calculate E(X) and E(Y):2 marks)Find the conditional density function fxi(cly). If applicable; state the interval(s for which your function applies; and the value of fx

Question 1 (10 marks) Let the two random variables X and Y have the following joint probability density function (pdf) k + y; if 0 < I < 2,2 < y < 1 fx(â‚¬,y) = 0; otherwise Draw diagram of the joint sample space of X and Y. mark b) Show that k 2 marks) Find the marginal probability density functions fx (1) and fy (y). 2 marks) Calculate E(X) and E(Y): 2 marks) Find the conditional density function fxi(cly). If applicable; state the interval(s for which your function applies; and the value of fxjy (xly) outside the interval(s) You do not need to calculate fyix(ylx). mark) Find the conditional expectation E(XIY ) mark Are X and Y independent? Justify your answer mark)

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