There are two traffic lights on a commuter's route to and from work. Let X₁ be the number of lights at which the commuter must stop on his way to work, and X₂ be the number of lights at which he must stop when returning from work. Suppose that these two variables are independent, each with the pmf given in the accompanying table (so X₁, X₂ is a random sample of size n = 2).

μ = 1, σ² = 0.6

Calculate σ_To².

σ_To² =

How does it relate to σ², the population variance?

σ_To² =  · σ²

(d)

Let X₃ and X₄ be the number of lights at which a stop is required when driving to and from work on a second day assumed independent of the first day. With T_o = the sum of all four X_i's, what now are the values of E(T_o) and V(T_o)?

E(T_o)=V(T_o)=

(e)

Referring back to (d), what are the values of

P(T_o = 8) and P(T_o ≥ 7)

[Hint: Don't even think of listing all possible outcomes!]

P(T_o = 8)

=

P(T_o ≥ 7)

=

8. Madsen Motors's bonds have 23 years remaining to maturity. Interest is paid annually, they have a $1,000 par value, the coupon interest rate is 7%, and the yield to maturity is 9%. What is the bond's current market price? Round your answer to the nearest cent.

9. A bond has a $1,000 par value, 10 years to maturity, and a 7% annual coupon and sells for $985.

1. What is its yield to maturity (YTM)? Round your answer to two decimal places.

10. Nesmith Corporation's outstanding bonds have a $1,000 par value, a 6% semiannual coupon, 12 years to maturity, and a 10% YTM. What is the bond's price? Round your answer to the nearest cent.

11. A firm's bonds have a maturity of 10 years with a $1,000 face value, have an 8% semiannual coupon, are callable in 5 years at $1,049.23, and currently sell at a price of $1,095.02. What are their nominal yield to maturity and their nominal yield to call? Do not round intermediate calculations. Round your answers to two decimal places.

The following data lists the ages of a random selection of actresses when they won an award in the category of Best​ Actress, along with the ages of actors when they won in the category of Best Actor. The ages are matched according to the year that the awards were presented. Complete parts​ (a) and​ (b) below.

Actress (years) 31   25   29   31   35   25   25   42   30   32

Actor (years)    56   40   39   34   29   37   52   35   34   44

a. Use the sample data with a 0.01 significance level to test the claim that for the population of ages of Best Actresses and Best​ Actors, the differences have a mean less than 0​ (indicating that the Best Actresses are generally younger than Best​ Actors).

In this​ example, μd is the mean value of the differences d for the population of all pairs of​ data, where each individual difference d is defined as the​ actress's age minus the​ actor's age. What are the null and alternative hypotheses for the hypothesis​ test?

H0​: μd (1) _____ , _____ years

H1​: μd (2) _____ , _____ years

​(Type integers or decimals. Do not​ round.)

(1) >

<

≠

=

(2) <

=

≠

>

Identify the test statistic.

t= _____ ​(Round to two decimal places as​ needed.)

Identify the​ P-value.

​P-value=_____ ​(Round to three decimal places as​ needed.)

What is the conclusion based on the hypothesis​ test?

Since the​ P-value is (3) _____ the significance​ level, (4) _____ the null hypothesis. There (5)_____ sufficient evidence to support the claim that actresses are generally younger when they won the award than actors.

(3) less than or equal to

greater than

(4) reject

fail to reject

(5) is

is not

b. Construct the confidence interval that could be used for the hypothesis test described in part​ (a). What feature of the confidence interval leads to the same conclusion reached in part​ (a)?

The confidence interval is _____ ​year(s)<μd< _____ ​year(s).

​(Round to one decimal place as​ needed.)

What feature of the confidence interval leads to the same conclusion reached in part​ (a)?

Since the confidence interval contains (6) _____ (7) _____ the null hypothesis.

(6) zero,

only negative numbers,

only positive numbers,

(7) reject

fail to reject

Demand for walnut fudge ice cream at the Sweet Cream Dairy can be approximated by a normal distribution with a mean of 17 gallons per week and a standard deviation of 3.2 gallons per week. The new manager desires a service level of 90 percent. Lead time is two days, and the dairy is open seven days a week. (Hint: Work in terms of weeks.)

a-1. If an ROP model is used, what ROP would be consistent with the desired service level? (Do not round intermediate calculations. Round your final answer to 2 decimal places.)

ROP ______ gallons

a-2. How many days of supply are on hand at the ROP, assuming average demand? (Do not round intermediate calculations. Round your final answer to 2 decimal places.)

Days _______

b-1. If a fixed-interval model is used instead of an ROP model, what order size would be needed for the 90 percent service level with an order interval of 7 days and a supply of 8 gallons on hand at the order time? (Do not round intermediate calculations. Round your final answer to the nearest whole number.)

Order size _______ gallons

b-2. What is the probability of experiencing a stockout before this order arrives? (Do not round intermediate calculations. Round your final answer to the nearest whole percent. Omit the "%" sign in your response.)

Probability _________ %

c. Suppose the manager is using the ROP model described in part a. One day after placing an order with the supplier, the manager receives a call from the supplier that the order will be delayed because of problems at the supplier’s plant. The supplier promises to have the order there in two days. After hanging up, the manager checks the supply of walnut fudge ice cream and finds that 2 gallons have been sold since the order was placed. Assuming the supplier’s promise is valid, what is the probability that the dairy will run out of this flavor before the shipment arrives? (Do not round intermediate calculations. Round your final answer to the nearest whole percent. Omit the "%" sign in your response.)

Risk probability _________ %

Step 4:

What percent of the variation in corn yield is explained by these two variables? Give your answers to 2 decimal places and do not include units in your answers.

Percent explained by the model = %

Step 5:

Using the regression equation, find a point estimate for the corn yield for 2014 Assume that the soy bean yield for that year is 42.

Point Estimate = (Give your answer to 1 decimal place.)

ID      Year    CornYield       SoyBeanYield
1       1957    48.3    23.2
2       1958    52.8    24.2
3       1959    53.1    23.5
4       1960    54.7    23.5
5       1961    62.4    25.1
6       1962    64.7    24.2
7       1963    67.9    24.4
8       1964    62.9    22.8
9       1965    74.1    24.5
10      1966    73.1    25.4
11      1967    80.1    24.5
12      1968    79.5    26.7
13      1969    85.9    27.4
14      1970    72.4    26.7
15      1971    88.1    27.5
16      1972    97      27.8
17      1973    91.3    27.8
18      1974    71.9    23.7
19      1975    86.4    28.9
20      1976    88      26.1
21      1977    90.8    30.6
22      1978    101     29.4
23      1979    109.5   32.1
24      1980    91      26.5
25      1981    108.9   30.1
26      1982    113.2   31.5
27      1983    81.1    26.2
28      1984    106.7   28.1
29      1985    118     34.1
30      1986    119.4   33.3
31      1987    119.8   33.9
32      1988    84.6    27.0
33      1989    116.3   32.3
34      1990    118.5   34.1
35      1991    108.6   34.2
36      1992    131.5   37.6
37      1993    100.7   32.6
38      1994    138.6   41.4
39      1995    113.5   35.3
40      1996    127.1   37.6
41      1997    126.7   38.9
42      1998    134.4   38.9
43      1999    133.8   36.6
44      2000    136.9   38.1
45      2001    138.2   39.6
46      2002    129.3   38.0
47      2003    142.2   33.9
48      2004    160.3   42.2
49      2005    147.9   43.1
50      2006    149.1   42.9
51      2007    150.7   41.7
52      2008    153.9   39.7
53      2009    164.7   44.0
54      2010    152.8   43.5
55      2011    147.2   41.9
56      2012    123.4   39.8
57      2013    158.8   43.3

Jennifer Nguyen, a Humber College Healthcare Management program graduate who always had only perfect marks in statistics, was hired by the famous Healthy Lifemedical insurance company. Jennifer is assigned to conduct statistical analysis of medical and financial data. As Jennifer is on probation, please help her to complete the following six tasks. In problems 2-6, state hypotheses H₀and H₁and provide detailed conclusions (based on P-values or critical values/test statistics) together with the Exceloutput. For your convenience the data are given in the Major Assignment Data file. You can also find useful information on the Blackboard in Excel Instructions folder. Jennifer’s manager Dr. Jonathan Steinberg, who has degrees and publications in both mathematical statistics and medical science, asked her to find estimates of the average dental claim reimbursement for 2019. As Healthy Lifehas many thousands of clients it is virtually impossible to calculate the population mean. Using the Excel Random Number Generator function, Jennifer found a random sample of 52 dental claims submitted to Healthy Life. The amounts covered by insurance you can see in the Major Assignment Data file. Please help Jennifer Nguyen to construct90%,95%, and 99%confidence intervals for the true average reimbursement. Make sure that t-distribution is applicable: build a histogram with the bin values, for example, $100, $200, $300, $400, and $500, and check whether it is approximately symmetric and bell-shaped. Then, use Descriptive Statistics function from Data Analysis. Constructing confidence intervals, please round values to two decimal places.

1. A manager wishes to check the miles her taxi cabs are driven each day. Her findings are shown below. Construct a frequency distribution, using ten classes.

   136	97	163	118	146	109	99
   124	119	151	122	131	124	101
   118	118	119	142	124	137	106
   152	99	107	151	139	116	137
   143	105	99	125	108	160	142

   What is the Range? Blank 1

   What is the Class Width? Blank 2

   Fill in the table after creating it on paper. rf and crf are rounded to two decimal places. To input the Class Limits and Class Boundaries, you will need to put the lower class limit/boundary in the first blank and the upper class limit/boundary in the blank below where you input the lower. It is the way the Blackboard tool works.

   Class Limits	Class Boundaries	Midpoints	f	cf	rf	crf
   Blank 3-Blank 4	Blank 5-Blank 6	Blank 7	Blank 8	Blank 9	Blank 10	Blank 11
   Blank 12-Blank 13	Blank 14-Blank 15	Blank 16	Blank 17	Blank 18	Blank 19	Blank 20
   Blank 21-Blank 22	Blank 23-Blank 24	Blank 25	Blank 26	Blank 27	Blank 28	Blank 29
   Blank 30-Blank 31	Blank 32-Blank 33	Blank 34	Blank 35	Blank 36	Blank 37	Blank 38
   Blank 39-Blank 40	Blank 41-Blank 42	Blank 43	Blank 44	Blank 45	Blank 46	Blank 47
   Blank 48-Blank 49	Blank 50-Blank 51	Blank 52	Blank 53	Blank 54	Blank 55	Blank 56
   Blank 57-Blank 58	Blank 59-Blank 60	Blank 61	Blank 62	Blank 63	Blank 64	Blank 65
   Blank 66-Blank 67	Blank 68-Blank 69	Blank 70	Blank 71	Blank 72	Blank 73	Blank 74
   Blank 75-Blank 76	Blank 77-Blank 78	Blank 79	Blank 80	Blank 81	Blank 82	Blank 83
   Blank 84-Blank 85	Blank 86-Blank 87	Blank 88	Blank 89	Blank 90	Blank 91	Blank 92

Assignment Purpose

Write a well commented java program that demonstrates the use and re-use of methods with input validation.

Instructions

1. It is quite interesting that most of us are likely to be able to read and comprehend words, even if the alphabets of these words are scrambled (two of them) given the fact that the first and last alphabets remain the same. For example,

“I dn'ot gvie a dman for a man taht can olny sepll a wrod one way.” (Mrak Taiwn)

“We aer all moratls, Hamrbee is an immoratl, and tehre is no question abuot it.” (Kevin Unknown)

2. Write a method named scramble that returns a String and takes a String as an argument.
   1. The argument is actually a word (of length 6 or more).
   2. It then constructs a scrambled version of that word, randomly flipping two characters other than the first and last one.
3. Then write the main method in which you would read the word from the user, send it to scramble, and print the scrambled word.
   1. You can use a loop to read multiple words if you like but it is not necessary.
   2. If the length of the entered word is less than 6, you should keep prompting the user to enter a valid word.
4. After writing all the comments, generate a Javadoc and submit it with the java file.

Hint: First generate two random integers in range of the length of the string. Then use substring method to access characters at those locations. Rest is left to your imagination.

Submission

A .java and a .html (generated with Javadoc) file