Q4 If the price of Pepsi increases, and the demand for Sprite increases as a result, which of the following is true? (1 point)

a. Pepsi is an inferior good and Sprite is a normal good

b. Pepsi and Sprite are complements

c. Pepsi is a normal good and Sprite is an inferior good

d. Pepsi and Sprite are substitutes

e. The law of demand has been violated

11. If you discover that both the equilibrium price and quantity of peas has risen, what would you conclude? (Hint : Try drawing the situations) ( 2 points ) a. Demand has decreased with supply remaining the same

b. Supply has decreased with demand remaining the same

c. Demand has increased with supply remaining the same

d. Supply has increased with demand remaining the same

12. Now suppose you find that you made a mistake. The equilibrium price and quantity of peas has actually fallen. What would you conclude now? (1 points ) a. Demand has decreased with supply remaining the same

b. Supply has decreased with demand remaining the same

c. Demand has increased with supply remaining the same

d. Supply has increased with demand remaining the same

X and y are discrete random variables. The only possible combinations of these two variables have the following probabilities: X 0 2 0 N/ H 0 16 y 1 0 0 2 1 O 16 (i) Show that X and Y are: (a) not independent ( b ) not uncorrelated. [4] (ii) State the circumstances under which the result E(X) = E[E(X | Y)] holds. [1] (iii) Calculate: (a) E(X +Y|X=1) (b) E(X|Y=2) (c) var(X | Y =2). [7] (iv) Determine the values of the random variable E[Y| X] and hence calculate E[E(Y2 1X)].[3] (v) Calculate E[Y '] and comment on your answer. [2] [Total 17]Determine: (i) P(Fg,24 a) =0.95. [1 [Total 3) Suppose that a random sample of nine observations is taken from a normal distribution with mean / =0. Let X and S' denote the sample mean and variance respectively. Determine (to 2 decimal places) the probability that the value of X exceeds that of S, ie determine P(X > S). [3] The waist measurements (in cm) of six male patients before and after undergoing a medically controlled diet are as follows: Patient 1 Patient 2 Patient 3 Patient 4 Patient 5 Patient 6 Before 106 98 110 100 105 96 After 98 97 82 89 80 90 Calculate a 90% confidence interval for the reduction in waist measurement following the diet. [3 A random sample of size 2n is taken from a geometric distribution for which: P(X =x)= pq*-1 x =1, 2,... Give an expression for the likelihood that the sample contains equal numbers of odd and even values of X . [3 A random sample of 16 observations ( x1,...,*16 ) from a normal distribution gives: 16 x, = 128 x7 =1,168 1=1 1=1 Calculate a 90% confidence interval for the population standard deviation