Let X and Y have the joint probability density function (pdf):

f(x, y) = 3/2 x²(1 − y),        − 1 < x < 1,      − 1 < y < 1

1. Find P(0 < Y < X).
2. Find the respective marginal pdfs of X and Y. Are X and Y independent?
3. Find the conditional pdf of X give Y = y, and E(X|Y = 0.5).

2. Suppose you are given the IS-LM model below: (1) C = 120 + 0.8YD (2) I = 300 – 2000r (3) G = 500 (4) T = 400 (5) YD = Y – T (6) Ms = 200 (7) Md = 80 + 0.1Y – 2000r

a. Find the equilibrium values of income and the interest rate.

b. Suppose you are again given equations (1) – (7), but equation (7) were to be replaced by: (7’) Md = 80 + 0.1Y Solve for the new equilibrium values of income and the interest rate

c. Using IS-LM, show graphically and discuss how the equilibrium income and interest rate differs when using equation (7’) rather than equation (7). In which case does an increase in government spending have a larger impact on income? Show graph corresponding to question (c):

Comprehensive Problem 2

Part 1 and Part 2:

Palisade Creek Co. is a merchandising business. The account balances for Palisade Creek Co. as of May 1, 2016 (unless otherwise indicated), are as follows:

Part 1: Using the attached spreadsheet, enter the balances of each of the accounts in the appropriate balance column of a four-column account. Write Balance in the item section, and place a check mark (√) in the Posting Reference column. Journalize the transactions for May, the last month of the fiscal year, below.

Part 2: Post the journal to the general ledger you created in Part 1, extending the month-end balances to the appropriate balance columns after all posting is completed. In this problem, you are not required to update or post to the accounts receivable and accounts payable subsidiary ledgers.

For a compound transaction, if an amount box does not require an entry, leave it blank or enter "0".

May 1: Paid rent for May, $5,000.

Comprehensive Problem 2
Part 4 and 6:

Note: You must complete parts 1, 2 and 3 before attempting to complete part 4 and part 6. Part 5 is an optional work sheet.

4. At the end of May, the following adjustment data were assembled. Analyze and use these data to complete Part 6.

6. Journalize the adjusting entries. For a compound transaction, if an amount box does not require an entry, leave it blank or enter "0". Post the adjusting entries to the attached spreadsheet you used in parts 1 and 2.

Comprehensive Problem 2

Part 7:

You must complete parts 1, 2, 3, 4 and 6 before completing part 7. Part 5 is the optional work sheet.

Prepare an adjusted trial balance. If an amount box does not require an entry, leave it blank or enter "0".

If a particle at rest decays into 2 lighter particles one of mass 1 MeVc^-2 traveling at 80 percent of the speed of light and the other at 2 MeVc^-2. Show that the original particle has a mass of 4.7 MeVc^-2.

Fit a quadratic function of the form ?(?)=?0+?1?+?2?2 f ( t ) = c 0 + c 1 t + c 2 t 2 to the data points (0,−1) ( 0 , − 1 ) , (1,8) ( 1 , 8 ) , (2,−7) ( 2 , − 7 ) , (3,−6) ( 3 , − 6 ) , using least squares.

Let R be the region inside x ^2 /9 + y^2 /25 = 1, with x ≥ 0. (That is, R is the right-hand side of the ellipse below.) (a) (15 pts) Use the change of variables x = 3u, y = 5v to transform ∫ ∫ R x dxdy to a polar coordinate integral. 3 −5 5 R (b) (5 pts) Evaluate the polar coordinate integral

1. Determine 2 sensor for detect uneven load on a ship!

2. Explain the working principle of the 2 sensors from number 1!

Find the line y = b + mx of best fit through the data {(.1, .2),(.2, .3),(.3, .7),(.5, .2),(.75, .8)}, using the least squares criterion.

(Use one of the software tools: Excel, SPSS, Mathematica, or MATLAB to answer the following items, and print out your results directly from the software)

An equation of a hyperbola is given.

y^2/36 - x^2/64 = 1

(a) Find the vertices, foci, and asymptotes of the hyperbola. (Enter your asymptotes as a comma-separated list of equations.)

(b) Determine the length of the transverse axis.

(c) Sketch a graph of the hyperbola.