Tag: Mathematics

1. Suppose that x1, x2, x3, x4, is a sample drawn from the uniform distribution f(x;θ):= 1/ θ if x∈[1,1+θ], or

0 otherwise,

where θ is an unknown parameter. Let y1, y2, y3, y4 be the associated order statistics.

(a) Find an expression for the joint likelihood function f(x1, x2, x3, x4; θ).

(b) Is y2 a sufficient statistic for θ? Give a brief explanation of your answer.

(c) Now suppose that x1 = 5, x2 = 3, x3 = 4, x4 = 2. Find the maximum likelihood estimate of θ.

(d) Using the values from part (c), find the method of moments estimate for θ. (Hint: there is only one parameter so you only need to compute the first moment).

2. Suppose that X1, . . . Xn are i.i.d. random variables with probability density function

f(x,θ) = θe^(−θx ) if x≥0 or 0 otherwise.

(a)Give an expression for the joint likelihood function f(x1, . . . , xn; θ).

(b) Show that the sample mean is a sufficient statistic for θ.

3. Suppose you collect a sequence of data points (x1,y1),…,(xn,yn) and you use least squares regression to find the values of α0 and α1 so that the line y = α1x + α0 gives the best match to the data. Show that if the data points already lie on a line y = mx+b i.e. (yi = mxi +b for i = 1, . . . , n), then least squares regression chooses the parameters α0 = b and α1 = m.

4. Suppose you are playing a random game that has three possible outcomes WIN, LOSE or DRAW. The probability of winning the game is an unknown parameter θ ∈ [0, 1], losing and drawing have equal probability 12 (1 − θ). Suppose you have a prior on the data that is given by h(θ) = 2θ.

(a) Suppose that it costs $5 to play the game, you get $15 dollars if you win, nothing if you draw, and you have to pay an additional $2 if you lose. Based on the prior distribution would you play the game? Explain.

(b) Now suppose you observe the following sequence of (independent) game out- comes: WIN, LOSE, DRAW, DRAW, WIN, LOSE, WIN, LOSE, DRAW, DRAW. Give an expression for the posterior distribution of θ.

(c) Based on the posterior distribution would you play the game?

(d) Would your answer to part (c) change if you had observed the following sequence of (independent) game outcomes instead: WIN, LOSE, LOSE, LOSE, WIN, LOSE, WIN, LOSE, LOSE, LOSE. Give a brief explanation of your reasoning.

Please see the attachment fr the questions 

Review the slideshow assignment. After reviewing the slideshow, answer the three questions provided. Remember to type and save your assignment as a Microsoft Word document and show all your work and explanations.

Hello. I was hoping that you would be able to help me solve a few problems as I have completed majority of it, but I am stuck on these last few. I have attached the questions that I need assistance with along with examples of the questions as a couple of them are two parts. Thank you

I’m working on a statistics spreadsheet and need an explanation to help me understand better.

Instructions

Scenario (information repeated for deliverable 01, 03, and 04)

A major client of your company is interested in the salary distributions of jobs in the state of Minnesota that range from $30,000 to $200,000 per year. As a Business Analyst, your boss asks you to research and analyze the salary distributions. You are given a spreadsheet that contains the following information:

• A listing of the jobs by title
• The salary (in dollars) for each job

Deliverable 3 – Confidence Intervals.xlsx

You have previously explained some of the basic statistics to your client already, and he really liked your work. Now he wants you to analyze the confidence intervals.

Background information on the Data

The data set in the spreadsheet consists of 364 records that you will be analyzing from the Bureau of Labor Statistics. The data set contains a listing of several jobs titles with yearly salaries ranging from approximately $30,000 to $200,000 for the state of Minnesota.

What to Submit

Your boss wants you to submit the spreadsheet with the completed calculations, answers, and analysis.

I’m working on a probability question and need an explanation and answer to help me learn.

a. 

Hypothesis testing for the comparison of two means can be confusing. What specific items have you found confusing about this week’s material? Are there any questions you would like answered? Why do you think there are so many methods for hypothesis testing for the comparison of two means? Why have to meet so many assumptions for testing? Could we reduce these situations to one formula?

b.

Discuss the difference between a Type I error and a Type II error in general for hypothesis testing. Is one type of error more detrimental than another? Why or why not? Does it depend on the situation? Could you provide an example?

11 questions in both pdf files attached
11 Quesions emphasizing vectors and dot products
Please answer every questions with clearly with workings shown.
**Will be given 8 hours but please send a midpoint progress pdf (4 hour mark) to show progress of what has been done 🙂

THIS IS STATISTICS NOT HISTORY WOULD NOT ACCEPT ANYTHING IN TITLE BUT THAT. WRITING QUESTION AT END ALSO: DESCRIBE HOW THESE CONCEPTS INTERSECT AND WHY SCALES OF MEASUREMENT INFLUENCE DECISIONS ABOUT STATISTICS AND GRAPHICS (4 TO 7 SENTENCES LONG)

Please finish the questions in excel. There are 2 sheets and contains one problem in each sheet.

PLEASE also write an explanation for it in a separate document.

Suppose the posterior distribution (pi_post) has a pdf k(theta|x_1,…x_n). Given c1,c2>0, consider the loss function

Please refer to picture for more details