Mathematics

Video link : https://www.dropbox.com/s/osgf0qw222dal1w/Wild_Planet.mov?dl=0What type of research design options and strategies are leveraged at Wild Planet?Are they using Exploratory, Descriptive or Causal Research Design techniques? What specific methodologies did you notice in the video?Is there anything further you would recommend for Wild Planet marketing management to give them the information to further grow their business?

1. A statistician has a sample X1, . . . , Xn from N(µ, ? 2). Also, the statis-tician has a sample Y1, . . . , Yk from an exponential distribution with param- eter ?. Suppose that these samples are independent. Find the variance of a random variable Z = 3X? ? 5Y? .2. Let a sample of size n from a distribution with the pdf f(x) be given. What is the pdf of X(1)?3. Let X1, . . . , Xn be independent RVs with E?(Xl) = l?. Consider an es- timator ?? =?n l=1 alXl. What condition should be imposed on a1, a2, . . . , anso that ?? is an unbiased estimator? 4. Let X1, . . . , Xn be iid Bernoulli with the probability of success ?. Sug-gest the minimal variance unbiased estimator, and then prove, using Cramer- Rao inequality, its efficiency.5. Consider a sample of size n from Unif(?, ?). Find (minimal) sufficient statistic for the pair (?, ?).6. Consider a sample of size n from Unif(0, ?). Find a method of mo- ments estimator of ?.7. Let we observe a sample X1, . . . , Xn where Xl = ? + Yl, with Yl being iid Expon(?). Find the MLE of ?. Hint: Do not forget about support of the exponential RV.8. For the problem 7, let ? be given. Find the MLE of cos(?). 9. Consider a sample of size n from Poisson(?). Find a method ofmoments estimator for the estimand ?2. 10. Let a sample of size n from N(?, ?2) be given. A statistician believes

1.) Consider the two-round bargaining game. The minimum the seller will sell his home for 188,000 and the maximum the buyer is willing to pay is $200,000. Both players know these two amounts and are bargaining over the difference (M=$12,00). Assume the disagreement values are zero for both players. Player 1 moves first by making a proposal and Player 2 can accept and reject. If player 2 rejects Player’s 1 proposal, then Player 2 gets to make a proposal, which Player 1 can reject and accept. The game is then over. Suppose the both players discount the future income at the rate d=0.2 per period. That is, $0.20 now is equivalent to $1,00 received next round. Find the equilibrium for this 2-round game. What is the sale price of the home? Which player gets the larger share of M?2.) In Depositor versus Saving & Loan Association (S&L), suppose that the S&L can invest $100,000 in a junk bond (the official name for this sort of security is high-yield bond) with the following rates of return: with high effort (H represents high research effort), the probability is 0,98 that the rate of return is 15% and 0.02 that the money vanishes; with low effort (L represents low research effort), the probability is 0.92 that the rate of return is 15% and 0.08 that the money vanishes. The rate of return on government bonds is 4%. After paying off the depositor, the S&L is left with $2000 minus research cost. Draw the extensive form and solve. Where should the depositor put the money?3.) Find time path (general solution) of P and U, given_P= (1/4) – 2U + n dP/dt = 1/2(P-n) dU/dt = – (m-p)4.) Consider a model of a competitive market in which price is adjust to excess demand or supply and firms enter or exit the industry if profits or losses are being made. Price adjusts to excess demand according to ?=(qD-qS), >0 where = a+bp is the demand function, =mN is the supply function, p is price, N is the number of firms in the industry, is speed-of adjustment coefficient. Making these substitutions gives ?=(a+bp-mN). The number of firms adjusts according to ?=z (p – ?), z>0 where ? is the fixed average cost of production. Firms enter (?>0) if price exceeds average cost (positive profits) and exit if price is less than the average cost (negative profit). Solve this system of differential equations for price and number of firms.5.) Suppose you have won $200,000 in the state lottery and you have decided to retire on your winnings. Suppose you deposit your winnings in a bank that pays 8% annual interest (compounded annually) and make yearly withdrawals of $30,000. (Hint: if periodic withdrawals, each of amount d, are deposited in a bank account whose initial amount is that pays interest at a rate r per period, then the difference equation that describes the total amount in the account after n periods is = (1+r) – d)a. What are the difference equation and initial condition that describes the future value of your account?b. Will you ever run out of money? If so, when?6.) Consider the following model, = s , = k ( – ), = where s is the marginal propensity to save and k is the acceleration coefficient. The third equation states the equilibrium condition for the determination of national income (ex ante saving = ex ante investment). Derive the general solution for . Comment on your result. (Let = for t=0)

This assignment is intended to help you learn how to apply statistical methods when analyzing operational data, evaluating the performance of current marketing strategies, and recommending actionable business decisions. This is an opportunity to build critical-thinking and problem-solving skills within the context of data analysis and interpretation. You’ll gain a first-hand understanding of how data analytics supports decision-making and adds value to an organization.Scenario:Pastas R Us, Inc. is a fast-casual restaurant chain specializing in noodle-based dishes, soups, and salads. Since its inception, the business development team has favored opening new restaurants in areas (within a 3-mile radius) that satisfy the following demographic conditions:Median age between 25 – 45 years oldHousehold median income above national averageAt least 15% college educated adult populationLast year, the marketing department rolled out a Loyalty Card strategy to increase sales. Under this program, customers present their Loyalty Card when paying for their orders and receive some free food after making 10 purchases.The company has collected data from its 74 restaurants to track important variables such as average sales per customer, year-on-year sales growth, sales per sq. ft., Loyalty Card usage as a percentage of sales, and others. A key metric of financial performance in the restaurant industry is annual sales per sq. ft. For example, if a 1200 sq. ft. restaurant recorded $2 million in sales last year, then it sold $1,667 per sq. ft.Executive management wants to know whether the current expansion criteria can be improved. They want to evaluate the effectiveness of the Loyalty Card marketing strategy and identify feasible, actionable opportunities for improvement. As a member of the analytics department, you’ve been assigned the responsibility of conducting a thorough statistical analysis of the company’s available database to answer executive management’s questions.Report:Write a 750-word statistical report that includes the following sections:Section 1: Scope and descriptive statisticsSection 2: AnalysisSection 3: Recommendations and ImplementationSection 1 – Scope and descriptive statisticsState the report’s objective.Discuss the nature of the current database. What variables were analyzed?Summarize your descriptive statistics findings from Excel. Use a table and insert appropriate graphs.Section 2 – AnalysisUsing Excel, create scatter plots and display the regression equations for the following pairs of variables:In your report, include the scatter plots. For each scatter plot, designate the type of relationship observed (increasing/positive, decreasing/negative, or no relationship) and determine what you can conclude from these relationships.Section 3: Recommendations and implementationBased on your findings above, assess which expansion criteria seem to be more effective.Could any expansion criterion be changed or eliminated? If so, which one and why?Based on your findings above, does it appear as if the Loyalty Card is positively correlated with sales growth? Would you recommend changing this marketing strategy?Based on your previous findings, recommend marketing positioning that targets a specific demographic. (Hint: Are younger people patronizing the restaurants more than older people?)Indicate what information should be collected to track and evaluate the effectiveness of your recommendations. How can this data be collected? (Hint: Would you use survey/samples or census?)

If I have two Products (Product A and Product B) and I want to ship these products to customers as follows:Product A (# of units: 4000)Product B (# of units: 4000)The products must be shipped through using Pallets.Each Pallet can hold 1000 units of Products A or 2000 units of Product B.Transportation cost for both Products (A and B) is the same. $1 dollar per pallet.Question: How many pallets I need to ship theses products? What is the final price the customer must for shipment?

CHAPTER 5: A SURVEY OF PROBABILITY CONCEPTSVideo #29: How to build a contingency table with Pivot table (Length: 3:40)Video #30: How to use Permut and Combin formulas (3:47)Video #31: How to apply Bayes Theorem (Length: 4:33CHAPTER 6: DISCRETE PROBABILITY DISTRIBUTIONSVideo #32: How to build and graph discrete probability distribution (Length: 3:36)Video #33: How to apply binomial distribution (Length: 4:48)Video #34: How to apply hypergeometric distribution (Length: 4:41)Video #35: How to apply Poisson.dist (Length: 3:31)

Respond to the following in a minimum of 175 words:In your opinion, how have statistics been used effectively by criminal justice professionals? Provide recommendations for more effective use and incorporation by criminal justice professionals.What are some examples of the effectiveness of criminal justice research in finding solutions to problems?

Payday LoansPayday loans are high-interest short-term loans, usually over a period of two weeks. One recurring political question is whether or not interest rates on such loans should be capped. Roughly speaking, those in favor of caps want to protect consumers from potentially harmful loans, while those against caps want to let the free market determine what the rate should be.1.) Watch the video and read the article below.Oliver, J. (2014). Predatory lending: Last week tonight with John Oliver. HBO.Retrieved from https://youtu.be/PDylgzybWAw(Note: the above video contains a high usage of profanity, please omit to view this video if you are offended by such language).Holland, J. (2016). Rapid City payday lender stops making loans due to new lower interest rates. Rapid City Journal.Retrieved from http://rapidcityjournal.com/news/local/rapid-city-payday-lender-stops-making-loans-due-to-new/article_0424e3da-5963-54f8-b5c3-60ba7797e743.html2.) Post a response of at least 150 words but not more than 350 words responding to the following.Do you think there should be interest rate caps on payday loans or not? Defend your answer.Determine the interest that would be charged on a two-week $300 payday loan if the interest rate is 520%, and the interest is compounded at the end of the two weeks. Explain how you came to your answer.Suppose a friend or family asked you how it could be possible that an annual interest rate is higher than 100%. Write out an explanation of what you might say to them.Be sure to give your answers in complete sentences.

Explain how to find coterminal angles. How does this process differ for angles given in radians verses angles given in degrees? For #15-18, find an angle between ?? and ???? coterminal to the given angle. Give your answer in radians. 16. &%!

mathnursingInstructionsIn this assignment, you will be required to use the Heart Rate Dataset to complete the following:Identify the variables in the datasetClassify each variable as qualitative or quantitative discrete or quantitative continuousSpecify the possible values of each variableGive a brief written description of what each variable tells us about the data provided.StepsOpen the Heart Rate Dataset in ExcelThere are 3 columns of data. Each column represents a different variable. What are the 3 variables represented in the dataset?Identify each of the 3 variables as qualitative, quantitative discrete, or quantitative continuousIdentify the possible values of each of the 3 variables in this dataset.Briefly describe what information each of the 3 variables tells us about the data