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 total budget that will be used for both A and/or B initiatives. The joint distribution for X and Y is given as:

fZ(x,y)= 15840*y^7*x^3 where 0[A] Consider the variable Z, if ward 9 of the city is responsible for paying 19th of the total budget, express 19th of Z as a function in terms of X and Y. 19Z(x,y)= (use lower case letters, in your expression) (If rounding use at least 5 digits after the decimal) [B] What is the total expected proportion of the budget to be paid for by ward 9? [C] What is the absolute value of the standard deviation of total expected proportion of the budget to be paid for by ward 9? [D] What is the Covariance of X and Y? [E] Are X and Y independent? A. Yes, because covariance is not 0 B. No, because covariance is not 0 C. Yes, because covariance is 0 D. No, because covariance is 0 E. Yes,because f(Y=y) f(X=x) = f(Y=y,X=x) [F] What is the distribution of Y? A. Beta (=4,=8) B. Beta (=8,=4) C. Beta (=8,=4+1) D. Beta (=8+1,=4+1) E. Beta (=4+1,=8+1) F. Beta (=4+1,=8) G. none of the above distributions describe Y [G] Let's say it was known/decided that 77% of the total budget is going to be spent on initiative B, what is the probability that between 9% and 16% of the total budget will be spent on initiative A?