Question

(1 point) A city is trying to assess what proportion of its budget to put into initiative A or initiative B. Citizens of the city were given an internet address where they could have their say and determine the proportion they would give to initiative A and B. They were also permitted to not allocate all/any funds to indicate that they would prefer to save the money for a different/future initiative. Consider three random variables: X- The proportion of the budget to be spent on initiative A Y- The proportion of the budget to be spent on initiative B Z- The proportion of the budget that will be spent on both A and B The joint distribution for X and Y is given as: fz(x, y) = 60yx? where 0 < x < 1,0 < y < 1, x + y < 1 Part (a) Consider the variable Z, express Z as a function in terms of X and Y. (use lower case letters) Part (b) What is the expected proportion of the budget to be spent on both initiatives? Part (c) The expected proportion of the budget to be spent of initiative A is? Part (d) The expected proportion of the budget to be spent of initiative B is? Part (e) What is the Covariance of X and Y?

Answer 1