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(a) What are the distributions of: (i)

; (ii)

; and (iii)

. (b) Prove or disprove that the expression of the asymptotic confidence interval

for

is

where

is the maximum likelihood estimate of

found in Question 1 (d)

Complete the square to solve the integral of x/sqrt x^2 +10x+30

Bruno, the consumer in Problem 1, is best friends with Ruby who shares Bruno's love for energy bars and smoothies. The accompanying table shows Ruby's utilities from smoothies and energy bars. \table[[Quantity of smoothies,Utility from smoothies (utils),Quantity of energy bars,Utility from energy bars (utils)],[0,0,0,0],[1,32,2,28],[2,60,4,52],[3,84,6,72],[4,104,8,88],[5,120,10,100]] The price of an energy bar is

, the price of a smoothie is

, and Ruby has

of income to spend. a. Which consumption bundles of energy bars and smoothies can Ruby consume if she spends all her income? Illustrate Ruby's budget line with a diagram, putting smoothies on the horizontal axis and energy bars on the vertical axis. b. Calculate the marginal utility of each energy bar and the marginal utility of each smoothie. Then calculate the marginal utility per dollar spent on energy bars and the marginal utility per dollar spent on smoothies. c. Draw a diagram like Figure

in which both the marginal utility per dollar spent on energy bars and the marginal utility per dollar spent on smoothies are illustrated. Draw the quantity of energy bars increasing from left to right, and the quantity of smoothies increasing from right to left. Using this diagram and the utility-maximizing principle of marginal analysis, predict which bundle - from all the bundles on her budget line - Ruby will choose.

1. Assume that the configuration space is represented by the Figure 1b, for the same 2 link manipulator with a different position of a point (negligible size) obstacle. Find the position of the point obstacle. (2 points)

Sea surface temperature (SST) controls tropical Pacific precipitation because warm water drives atmospheric convection. When SST exceeds 27-28C, the ocean surface evaporates large amounts of water vapor and heats the covering air, causing it to rise rapidly. As this warm, moist air rises, it cools and water vapor produces heavy rainfall. Precipitation therefore concentrates where the warmest water is located, during normal conditions, the western Pacific's warm pool generates intense rainfall over Indonesia, while the cooler eastern Pacific remains dry. During El Nino, when warm waters shift eastward, the rainfall zone shifts with them and it brings floods to places like Peru and droughts to places like Indonesia. Precipitation follows the warmest SSTs because only sufficiently warm ocean surfaces provide the energy needed to fuel and produce tropical rainfall. Using the provided blank maps, create three precipitation intensity maps for the conditions you identified above. Use colors or symbols to show areas of high and low precipitation, and include a legend that explains your symbols and colors. Connect the profiles to scenarios identified above (contour maps). 20n 10n 0 10s 20 s AND 100 e 140 e 180 140w 100w 60 w SHOW ON MAP SHOWING EQUAOTIRAL PACIFIC REGION MOST IMPACTD BY ENSO CONDITIONS FOR NORMAL, EL NINO AND LA NINA

Is a bone an organ? Explain. How many bones in an average adult skeleton?

PROBLEM #14 14. (I) An electron is projected vertically upward with a speed of

into a uniform magnetic field of 0.480 T that is directed horizontally away from the observer. Describe the electron's path in this field.

Q2. For the beam shown in Figure Q2, find the bending stress at (a) point A and (b) point B. The beam is subjected to a moment

as shown in Figure Q2(b). [40 marks] Figure Q2

Economics: Its very SERIOUS IF you give aagainna ai answers ,i give mutiple dislikes The rent for apartments in a city is determined at an equilibrium of $1,000 per month, with demand and supply both at 2,000 units. The government fixes a maximum rent of $800. At this price, the number of apartments demanded rises to 2,500, but only 1,600 are supplied. The housing board wants to know the shortage in the rental market. Calculate the shortage.

Economics: Its very SERIOUS IF you give aagainna ai answers ,i give mutiple dislikes In the egg market, equilibrium is at $2 per egg, with demand and supply both at 5,000 eggs. The government fixes a maximum price of $1.50. At this price, demand increases to 6,000 eggs, but supply decreases to 4,000 eggs. The poultry association wants to know the shortage. Calculate the shortage.