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6. The joint pdf fxy (a, b) is zero outside the triangular region shown below and is equal this joint pdf: to a fixed number y on the triangular region. Answer the following questions about (a) Calculate the value of y. (b) Are X and Y independent? Prove your answer and then intuitively explain why you think they are independent or dependent. (c) Calculate cov( X, Y). Does the result you obtain make sense? (d) Define Z = X2. Calculate the joint CDF Fzy (a, b) (e) Define Z - X2. Calculate cov( Z, Y). Compare this result with the result of part (c) and intuitively explain if both results make sense. (f) Calculate the CDF of X - Y. (g) Calculate the joint CDF of two random variables Z = X + Y and W = X - Y.6. The joint pdf fxy (a, b) is zero outside the triangular region shown below and is equal this joint pdf: to a fixed number y on the triangular region. Answer the following questions about (a) Calculate the value of y. (b) Are X and Y independent? Prove your answer and then intuitively explain why he you think they are independent or dependent. (c) Calculate cov( X, Y). Does the result you obtain make sense? (d) Define Z = X2. Calculate the joint CDF Fzy (a, b). (e) Define Z - X2. Calculate cov( Z, Y). Compare this result with the result of part (c) and intuitively explain if both results make sense. (f) Calculate the CDF of X + Y. (g) Calculate the joint CDF of two random variables Z = X + Y and W = X - Y