Let X denote the number of Canon SLR cameras sold during a particular week by a certain store. The pmf of X is

x 0 1 2 3 4

pX(x) 0.1 0.2 0.3 0.25 0.15

Seventy percent of all customers who purchase these cameras also buy an extended warranty. Let Y denote the number of purchasers during this week who buy an extended warranty.

(a) What is P(X = 4, Y = 2)? [Hint: This probability equals P(Y = 2|X = 4) · P(X = 4); now think of the four purchases as four trials of a binomial experiment, with success on a trial corresponding to buying an extended warranty.] (Round your answer to four decimal places.)

P(X = 4, Y = 2) =

(b) Calculate P(X = Y). (Round your answer to four decimal places.)

P(X = Y) =

(c) Determine the joint pmf of X and Y. y x (0.7)y(0.7)x−y · pX(x) x y (0.7)y(0.3)x−y · pX(x) x y (0.7)x(0.3)x−y · pX(x) y x (0.7)x(0.7)x−y · pX(x)

Determine the marginal pmf of Y. (Round your answers to four decimal places.)

y 0 1 2 3 4

pY(y)

Please show work.

Molecular Orbital Theory -- Homodiatomics Use the molecular orbital model to fully describe the bonding in O2+, O2, O2-, and O22-. Determine which of the following statements are true and which are false.

The electron configuration of O2- is (σ2s)2(σ2s*)2(σ2p)2(π2p)4(π2p*)

The electron configuration of O2+ is (σ2s)2(σ2s*)2(σ2p)2(π2p)4(π2p*)

The number of unpaired electrons in O2+ and O22- is, respectively, 1 and 2.

The bond lengths increase in the order: O2+ < O2 < O2- < O22-.

The bond order in O2+ and O2 is, respectively, 2.5 and 2.

Bond length and bond energy both increase with increasing bond order.

Suppose X1, X2, ..., Xn is a random sample from a Poisson distribution with unknown parameter µ.

a. What is the mean and variance of this distribution?

b. Is X1 + 2X6 − X8 an estimator of µ? Is it a good estimator? Why or why not?

c. Find the moment estimator and MLE of µ.

d. Show the estimators in (c) are unbiased.

e. Find the MSE of the estimators in (c).

Given the frequency table below:

X 0 1 2 3 4 5 6 7 8

Frequency 1 4 8 10 8 7 5 4 1

f. Given n = 48, calculate one estiamte of µ.

1: State how many significant figures there are in each of the following calculations, and indicate which is the limiting value:

Part (a) (18.7)^2:

^1- 1 (limited by 2)

^2-4 (limited by 18.7

^3- 2 (limited by 18.7

^4- 3 (limited by 18.7)

^5- None of these.

Part (b) (1.60 × 10^-19)(3712) :

1- 2 (limited by 3712)

2- 2 (limited by 1.60)

3- 4 (limited by 3712)

4- 3 (limited by 1.60)

5- None of these.

2: A student witnesses a flash of lightning and then t = 2.5 s later the student hears the associated clap of thunder.

Part (a) Sound travels at 343 m/s in the air. What distance from the student is the lightning strike, in meters?

Part (b) Light travels at 3.0 × 10⁸ m/s in the air. How long, t₁, in seconds did it take the light to reach the student's eyes after the lightning strike?

3: On a two-leg trip, a car travels the first leg, a distance D₁ = 49 miles, in a time t₁ = 1.1 hours, and travels the second leg, a distance D₂ = 140 miles, in time t₂ = 2.25 hours. Refer to the figure.

Part (d) What is the average speed for the whole trip in meters per second?

4: A student begins at rest and then walks north at a speed of v₁ = 0.55 m/s. The student then turns south and walks at a speed of v₂ = 0.92 m/s. Take north to be the positive direction. Refer to the figure.

Part (a) What is the student's overall average velocity v_avg, in meters per second, for the trip assuming the student spent equal times at speeds v₁ and v₂?

Part (b) If the student travels in the stated directions for 30.0 seconds at speed v₁ and for 20.0 seconds at speed v₂, what is the net displacement, in meters, during the trip?

Part (c) If it takes the student 5.0 s to reach the speed v₁ from rest, what is the magnitude of the student’s average acceleration, in meters per second squared, during that time?

Import the text into Excel. The column delimiter is the minus sign, ‘-‘. Make a table of the total population of each city in each state in excel and post all steps used.

State Code-County Code-City Code-Population
2-117-13-49174
4-134-21-72247
3-137-27-91811
8-140-13-13913
4-133-16-11028
1-119-12-37710
10-101-31-76485
8-138-16-82956
6-125-26-67320
2-108-19-27973
6-119-22-25359
8-122-17-16881
4-140-18-63178
2-111-13-53192
2-112-30-31156
1-127-19-37547
9-135-23-48125
3-108-19-61645
6-113-26-16166
5-112-31-17847
7-135-23-48441
5-124-15-20688
6-106-15-95046
3-105-16-35144
6-120-29-97858
9-117-26-19441
6-120-18-71854
2-114-24-80466
3-138-15-73195
3-104-28-62538
1-133-24-74205
2-126-11-56200
3-129-15-41400
8-121-21-13075
10-138-19-57237
8-112-21-99683
2-114-13-70453
4-113-28-33874
9-112-23-23172
6-105-18-74177
7-140-21-11851
1-115-28-28103
5-134-20-48211
6-114-20-51120
3-111-24-55273
7-119-28-19041
8-122-29-19288
3-134-11-94750
9-119-26-62117
6-138-21-66254
4-117-29-21650
2-135-28-31025
5-135-24-30519
10-118-27-22788
9-102-19-92033
1-138-22-49667
2-101-24-81847
3-122-20-13381
3-124-18-34141
6-140-17-52557
6-131-28-23671
2-126-12-15206
7-124-23-28605
10-101-23-85366
10-106-19-57824
4-132-21-53104
3-119-29-51525
4-107-30-53327
5-108-17-97390
5-128-26-24022
3-117-19-37134
7-135-17-64097
3-140-31-93398
10-129-19-30970
2-112-12-85156
6-136-29-52765
5-121-21-73339
4-113-27-54497
8-113-22-94934
8-138-12-51563

A well-researched effect in the criminal justice literature is that mock jurors in research studies are more likely to convict an African-American defendant than a White defendant when they are accused of the same crime. For this study, we wanted to know whether a measure of self-reported racial bias was correlated with or could be used to predict harshness of sentencing recommendations for an African-American defendant. Participants read a vignette where an African American defendant was tried and convicted of a crime, and they were then asked to indicate how long of a prison sentence they felt he deserved (options ranged from 0 years – 7 years). They then completed a measure of self-reported racial bias, which had a minimum score of 0 (least biased) to 20 (most biased)

Enter the following data set into SPSS.

1. Create a scatterplot in SPSS to look at the relationship between the two variables and include it with your output. What would you say the relationship between the two variables is? (strength and direction) __________________________________  
2. Now run an analysis to determine whether there is a significant correlation between the two variables. Which type of SPSS analysis is appropriate to use to answer the question above? _____________________
3. What is the mean for racial bias? __________ What is the mean for sentencing recommendations? _________
4. What is the correlation between racial bias and sentencing recommendations? __________________ Is it significant at a = .05? ______________
5. How would you describe this correlation? (strength and direction) ________________________________

1. Compute the marginal products of the first through the eighth units of labor and enter them in the table. (It may be easiest to just copy and paste this whole page into your submission and complete it there.)

Marginal      Average
Units of Total product       product
labor production   of labor of labor

   0    0 0 0

   1    80 _____         _____

   2 200 _____         _____

   3 330 _____         _____

   4 400 _____         _____

   5 450 _____         _____

   6 480 _____         _____

   7 490 _____         _____

   8 480 _____         _____

2. Now compute the average products of the various quantities of labor and enter them in
the table.

3. There are increasing returns to labor from the first through the __________ units of labor and
decreasing returns from the __________ through the eighth units.

Second exercise (entirely new set of data, you're through with the table you just completed)

Now use the data given in the following table. The fixed cost of the firm is $500, and the firm’s total variable cost is indicated in the table.

Output   Total variable cost (TVC)

1                                         $?200

   2 360

   3 500

   4 700

   5 1000

   6 1800

a. Calculate average variable cost for 4 units of output.

b.Calculate average total cost for 4 units of output.

1. Your hapless statistics professor and the National Association of Pillow-makers (NAP) have asked you to investigate the insidious impact of caffeine consumption on student-professor relations. To study the topic you collect the following information about the number of cups of coffee consumed by a sample of students in a given day during finals week and the number of violent thoughts they have about their professors.

              Student #        Cups of coffee         Violent thoughts

              1                                6                             5

              2                                3                             2

              3                                2                             8

              4                                4                             9

              5                                3                             3

              6                                0                             1

              7                                1                             4

              8                                5                             6

              9                                7                             7

              10                              4                             0

1. With a single statistic, summarize the strength and the direction of the association between the number of cups of coffee consumed and the number of violent thoughts for this group of students. Be sure to name and interpret the statistic you use.
2. Do your data provide enough evidence to conclude that the association between coffee consumption and violent thoughts exists in the population from which your sample was drawn? (Again, you will need to perform a hypothesis test.) Explain your answer and show all necessary work. You should write out the research and null hypotheses in Greek notation.

Tim and Tam respectively invested $55 000 and $45 000 to form T & T Partnership on 1 January 2019. The partnership had a final profit of $66 000 for the year ended 31 December 2019.

Required:

1. By using Method 2 (fixed capital balances) procedures, prepare the journal entries to close the Profit or Loss Summary account, and then to distribute the profit to partners Tim and Tam under each of the following assumptions:

1. Tim and Tam agree to share a profit in the ratio of 3:2. (4 marks)

2. Tim and Tam agree to share a profit in the ratio of their respective original capital investment. (4 marks)

3. Tim and Tam agree to recognise a respective salary allowance of $20 000 per year to Tim and $15 000 to Tam. In addition, each partner is entitled to 7% interest on his original capital investment, with the remaining profit to be equally shared.     (4 marks)

2. Repeat the above-mentioned requirement (1) (c), this time assuming T & T Partnership made a profit of only $38 000 for the year ended 31 December 2019.

(4 marks)

Show your relevant workings on the above requirements (1) and (2) to support your journal entries.

As the production manager of the Neptune Boat Corporation, you must determine how many units of the Model 4W speedboat to produce over the next four quarters. The company has a starting inventory of 75 units, and demand is 125 units in quarter 1, 100 units in quarter 2, 40 units in quarter 3, and 20 units in quarter 4. Production capacity is limited to 70 units in quarter 1, 90 units in quarter 2, 50 units in quarter 3, and 60 units in quarter 4. The inventory cost during quarters 1 and 2 is $200 per unit per quarter, and $300 per unit per quarter during quarters 3 and 4. Production costs for the first quarter are $8,000 per unit, and these costs increase by 10% per quarter due to increasing labor and material costs. Neptune’s senior management has indicated that the ending inventory for quarter 4 must be at least 30 units. Develop a linear programming model that Neptune can use to determine the optimal production schedule that will minimize the total cost of meeting demand for the Model 4W speedboat in each quarter, subject to the capacity and inventory constraints. You do not need to solve the LP.