Provide correct solutions to the following questions

QE=o+.a.a+c;3 (1) Q? = '10 + (113' + U? (2} P; is the price of banana, Q? is the supply of banana, Q\" is the demand of banana. US" and Us) are mutually independent IID random variables with a mean of zero: and variances equal to 03: and 03, respectively. Q? = Q? is the market equilibrium condition. (a) Show that R,- and U? are correlated. [15 points) (13) Show that. the OLE estimator of a] is biased. (5 points) Now, \"7e add a new explanatory variable K; into the demand function of banana. Y; describes the income level and is exogenous which means Y; is uncorrelated with both UP and UES. Q=o+aa+a3 (3) Q? = (1'0 +Ct'1pg' + 02K + U? (4) (c) \"Tith equation (3) (4) and the market equilibrium condition, write (2,: = 1T3 + 71'le + 83. Find 77%, rrf, and sf as functions of .30: .81, (10, CE], org, U53, and U159. (10 points) Recall our linear model : index$_$nsa; = Bo + By Homicides; + BRRobberies; + BA Assaults; + ; (2.2) and recall the the assumption that =1 , . . ., En " IN (0, 02). Bo Let 8 be the least square estimator of the vector B = BH BR BA What kind of distribution does B follow? Ot-distribution with 3 degrees of freedom t-distribution with 332 degrees of freedom Ox2-distribution with 3 degrees of freedom Ox2-distribution with 332 degrees of freedom Multivariate Gaussian distribution with mean BA firm's production function is given by Q =21 /* + 4K. ", where Q. L, and K denote the number of units of output, labour, and capital, respectively. Labour costs are $2 per unit, capital costs are $2 per unit, and output sells at $12 per unit. Find the profit function for this firm and hence determine the maximum profit and the values of L and K at which it is achieved. Give an expression for the profit function in terms of labour and capital. (Give your answer in index form using fractions for powers as needed ) For what values of L and K is profit maximised? K = (Give your answer to the nearest whole number.) What is the maximum profit? (Give your answer to the nearest dollar)Given the following table, which timeline chart illustrate the execution of the processes using Round Robin (RR) scheduling algorithm with the time quantum set to 3. Process Arrival Time CPU Cycle P1 0 P2 1 6 P3 2 3 P4 3 5 P5 4 7 O A. P1 P2 P3 P4 P5 P1 P2 P4 P5 P5 3 6 9 12 15 16 19 21 24 25 O B. PI P2 P3 P4 P1 P2 P4 P5 P5 P5 3 6 8 11 13 16 18 21 24 25 O C. P1 P2 P3 P4 P5 P1 P3 P4 P5 P5 O 3 6 8 11 14 15 18 20 23 25 O D. P1 P2 P3 P1 P4 P4 P5 P5 P2 P4 0 3 6 9 10 13 15 18 21 22 25