1.1 LetX∼Poisson(4). The r command dpois(0:9, 4) gives the probabilities that P(X=k) fork= 0,1,...,9.

1.1.1 Use the plot() function to plot these probabilities and to connect the points with lines.

1.1.2 Use the barplot() function to make a barplot these probabilities.

1.2 The r command rpois(1000, 4) generates a sample of 1000values from the Poisson(4) distribution. Use the barplot()function to plot the empirical probabilities for X=k resultingfrom this sample

please include r code needed to generate plots

Life Span of Tires: A certain brand of automobile tires has a mean life span of 35,000 miles and a standard deviation or of 2,250 miles. (Assume a bell-shape distribution).

1. The span of three randomly selected tires are 34,000 miles, 37,000 miles, and 31,000 miles. Find the z-scores that correspond to each life span. Would any of these tires be considered unusual?
2. The life spans of three randomly selected tires are 30,500 miles, 37,250 miles, and 35,000 miles. Using the Empirical Rule, find the percentile that corresponds to each life span.

An urn contains 7 black balls, 4 red balls, 3 white balls and 1 blue ball, and a player is to draw one ball. If it is black, he wins $1, if it is red, he wins $2, if it is white he wins $3 and if it is blue, he pay $25.

a. Set up the empirical probability distribution for the random variable X, the payoff of the game.

b. What is the mathematical expectation of this game?



c. In the long-run, will the player win or lose?

The semester average grade for a statistics course is 76 with a standard deviation of 5.5. Assume that stats grades have a bell-shaped distribution and use the empirical rule to answer the following questions (explain your responses with the help of a graph):

1. What is the probability of a student’s stat grade being greater than 87?

2. What percentage of students has stat grades between 70.5 and 81.5?

3. What percentage of students has stat grades between 70.5 and 65?

4. What is the probability of a student’s stat grade being greater than the mean?

1. [20 marks]  Does a market economy provide too little or too much incentive to undertake innovation?  Explain, identifying the criterion you are using to answer.  Identify the roles that competition and appropriability play in your answer.
2. [20 marks]  Does empirical evidence show that patents increase innovation rates or not?  Explain, citing evidence and measurement issues as appropriate.  
3. [10 marks]  Compare the static and dynamic welfare effects of using patents to incentivise innovation or, alternatively, using prizes to incentivise innovation. Point out both advantages and disadvantages of each method.  

Throughout the semester, you have learned about several theories and practices of psychology across many different areas. This assignment will give you an opportunity to apply some of those major concepts, theoretical perspectives, and empirical findings. In completing this assignment, you will hone your critical thinking skills, recognizing and applying psychological principles, and communicating your understanding of individual, community, and organizational life experiences to a general audience.

Task:

For this assignment, you will write a 3-5 page paper based on a film or book that you will explore through the application of psychological theory and research.

3. The average sale per customer at a department store is $120.00 with a standard deviation of $10.00.  

According to the Empirical Rule, the percentage of sales between

$90.00 and $150.00 would be   __________________

Using Chebyshev’s Theorem, the upper and lower limits for 75% of the data values =

_________to ___________.

c)    If a customer spends $160.00, which of the following is correct?

a) It is an outlier because it’s more than 3 standard deviations below the mean.

b) It is an outlier because it’s more than 3 standard deviations above the mean.

c) It is not an outlier.

d) None of the above is correct.

Actuary and trustee reports indicate the following changes in the PBO and plan assets of Douglas-Roberts Industries during 2018:

Actuary and trustee reports indicate the following changes in the PBO and plan assets of Douglas-Roberts Industries during 2018: Prior service cost at Jan. 1, 2018, from plan amendment at the beginning of 2015 (amortization: $5 million per year) $ 25 million Net loss—AOCI at Jan.1, 2018 (previous losses exceeded previous gains) $ 112 million Average remaining service life of the active employee group 10 years Actuary's discount rate 5 % ($ in millions) Plan PBO Assets Beginning of 2018 $ 800 Beginning of 2018 $ 600 Service cost 70 Return on plan assets, 6% (8% expected) 36.0 Interest cost, 5% 40.0 Loss (gain) on PBO (19 ) Cash contributions 106 Less: Retiree benefits (40 ) Less: Retiree benefits (40 ) End of 2018 $ 851.0 End of 2018 $ 702.0 Required: 1-a. Determine Douglas-Roberts' pension expense for 2018. 1.b, 2. to 4. Prepare the appropriate journal entries to record the pension expense, to record any 2018 gains and losses, to record the cash contribution to plan assets and to record retiree benefits.

On January 1, 2018, the Mason Manufacturing Company began construction of a building to be used as its office headquarters. The building was completed on September 30, 2019. Expenditures on the project were as follows: January 1, 2018 $1,280,000 March 1, 2018 720,000 June 30, 2018 920,000 October 1, 2018 720,000 January 31, 2019 288,000 April 30, 2019 621,000 August 31, 2019 918,000 On January 1, 2016, the company obtained a $3,200,000 construction loan with a 15% interest rate. The loan was outstanding all of 2018 and 2019. The company's other interest-bearing debt included two long- term notes of $3,000,000 and $7,000,000 with interest rates of 11% and 13%, respectively. Both notes were outstanding during all of 2018 and 2019. Interest is paid annually on all debt. The company's fiscal year- end is December 31. Required: 1)Calculate the amount of interest that Mason should capitalize in 2018 and 2019 using the specific interest method. 2)What is the total cost of the building? 3)Calculate the amount of interest expense that will appear in the 2018 and 2019 income statements.