Let's say that my utility function over wealth is LaTeX: U=\ln\left(W\right) U = ln ⁡ ( W ) where W is my wealth in dollars. Suppose I currently have $1,000,000 in wealth (oh ye-ah), but my friend Rob offers me an opportunity to invest in his new start-up creating autonomous window-washing robots. [Note: the robots part is a kinda-true story. Ask me sometime!] If the start-up is successful—and we estimate it has a 10 percent chance of success—Rob will pay me $2,000,000. If it fails, however, I am paid nothing. He offers me this opportunity at a price of $100,000 1.What is the expected value of this opportunity? 2.What is the expected *utility* of this opportunity? 3.Would I take Rob's offer given my risk preferences?

Scatterplot of daily cycling distances and type of climb: Every summer, the touring company America by Bicycle conducts the “Cross Country Challenge,” a 7-week bicycle journey across the United States from San Francisco, California, to Portsmouth, New Hampshire. At some point during the trip, the exhausted cyclists usually start to complain that the organizers are purposely planning for days with lots of hill and mountain climbing to coincide with longer distances. The tour staff counter that no relation exists between climbs and mileage and that the route is organized based on practical issues, such as the location of towns in which riders can stay. The organizers who planned the route (these are the company owners who are not on the tour) say that they actually tried to reduce the mileage on the days with the worst climbs. Here are the approximate daily mileages and climbs (in vertical feet), as estimated from one rider’s bicycle computer.

1. Construct a scatterplot of the cycling data, putting mileage on the x-axis. Be sure to label everything and include a title.
2. We haven’t yet learned to calculate inferential statistics on these data, so we can’t estimate what’s really going on, but do you think that the amount of vertical climb is related to a day’s mileage? If yes, explain the relation in your own words. If no, explain why you think there is no relation.
3. It turns out that inferential statistics do not support the existence of a relation between these variables and that the staff seems to be the most accurate in their appraisal. Why do you think the cyclists and organizers are wrong in opposite directions? What does this say about people’s biases and the need for data

What are chi distributions, how do we use them, when do we use them, and why are they important?

Compare the TF-IDF pivoted normalization formula and Okapi formula analytically.

Both formulas are given in the figure above. What are the common statistical information about documents and queries that they both use? How are the two formulas similar to each other, and how are they different?

.How does cellphone service compare between different cities? The data stored in CellService represents the rating of Verizon and AT&T in 22 different cities (Data extracted from “Best Phones and Services,” Consumer Reports, January 2012, p. 28, 37). Is there evidence of a difference in the mean cellphone service rating between Verizon and AT&T? (Use a 0.05 level of significance)

I WANT THE ANSWER IN EXCEL USING THE DATA ANALYSIS....DO NOT PROVIDE A HAND WRITTEN ANSWER...I'm trying to understand the functions in excel

Intro Discussion and Questions- Regression and Correlation:

1. How does correlation analysis differ from regression analysis? What are the goals of each?

2. What does the correlation coefficient r measure? Be specific. What values can it take on? What do

   the values indicate?

3. What values can the coefficient of determination take on? What does it measure?

4. What are some of the limitations of simple linear regression?

5. Describe the equation for multiple linear regression; be sure to clearly define all of its parts.

6. In a simple linear regression, the following regression equation is obtained :

   ? = ???−???+?.
   ?) Interpret the slope coefficient
   ?) Predict the response if ? = −??.

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In the product mix example in this chapter, Quick-Screen is considering adding some extra operators who would reduce processing times for each of the four clothing items by 10%. This would also increase the cost of each item by 10% and thus reduce unit profits by this same amount (because an increase in selling price would not be possible). Can this type of sensitivity analysis be evaluated using only original solution output, or will the model need to be solved again? Should Quick-Screen undertake this alternative? In this problem, the profit per shirt is computed from the selling price less fixed and variable costs. The computer solution output shows the shadow price for T-shirts to be $4.11. If Quick-Screen decided to acquire extra T-shirts, could the company expect to earn an additional $4.11 for each extra T-shirt it acquires above 500, up to the sensitivity range limit of T-shirts?

Plant Food Case

A garden center wishes to determine if there are in fact differences in the effect of three different brands of plant food on the growth of sunflowers and the rank of their effectiveness in promoting growth. To do so, they selected 15 sunflower seedlings at random from the greenhouse and fed 5 of the seedlings with Plant Food A, 5 with Plant Food B, and 5 with Plant Food C. The weekly growth of each seedling was measured in inches and is summarized below.

1. Describe the purpose of the study
2. Conduct a Single Factor Analysis of Variance Hypothesis Test at alpha =.05
3. Explain the method used to set up and conduct the test
4. Describe the results
5. State a conclusion
6. Justify the conclusion

Suppose N = 10 and r = 3.

Compute the hypergeometric probabilities for the following values of n and x. (Round your answers to four decimal places.)

n = 3, x = 3

n = 6, x = 3

There is a solution but the answers to these 2 questions are incorrect

Below are abundances of 2 pronghorn antelope herds over 19 consecutive years. Calculate the coefficient of variation for each herd and determine which herd, if any, has greater variation in population abundance. Report all R code used

GB: 40,27,32,33,39,24,18,17,13,13,19,21,19,25,33,34,23,17,15

LS: 50,57,62,54,53,47,34,43,46,49,41,36,45,44,48,50,47,59,60

Let's try putting the CLT (Central Limit Theorem) to practice. In a study of bumblebee bats, one of the world’s smallest mammals, the weights have a mean of 2.0 grams and a standard deviation of 0.25 gram.

a) Find the probability that a randomly selected bat from the study weights more than 2.3 grams.

b) A random sample of 7 bumblebee bats is selected from the study. Find the probability that the mean weight of the sample is more than 2.3 grams.

c) A random sample of 40 bumblebee bats is selected from the study. Find the probability that the mean weight of the sample is more than 2.3 grams.

On their farm, the Friendly family grows apples that they harvest each fall and make into three products—apple butter, applesauce, and apple jelly. They sell these three items at several local grocery stores, at craft fairs in the region, and at their own Friendly Farm Pumpkin Festival for 2 weeks in October. Their three primary resources are cooking time in their kitchen, their own labor time, and the apples. They have a total of 500 cooking hours available, and it requires 3.5 hours to cook a 10-gallon batch of apple butter, 5.2 hours to cook 10 gallons of applesauce, and 2.8 hours to cook 10 gallons of jelly. A 10-gallon batch of apple butter requires 1.2 hours of labor, a batch of sauce takes 0.8 hour, and a batch of jelly requires 1.5 hours. The Friendly family has 240 hours of labor available during the fall. They produce about 6,500 apples each fall. A batch of apple butter requires 40 apples, a 10-gallon batch of applesauce requires 55 apples, and a batch of jelly requires 20 apples. After the products are canned, a batch of apple butter will generate $190 in sales revenue, a batch of applesauce will generate a sales revenue of $170, and a batch of jelly will generate sales revenue of $155. The

Two teams A and B are playing against each other in a tournament. The first team to win 3 games is the champion. In each of the games, A has a probability of 0.25 to win, independent of the outcome of the previous games. Let random variable X represent the number of the games played.

(b) compute the PMF Px(x)

(d) During the tournament, team A was not able to win the tournament after the first 4 games. Compute the conditional PMF PX|X>4 (x)

You would like to study the height of students at your university. Suppose the average for all university students is 67 inches with a SD of 18 inches, and that you take a sample of 19 students from your university.

a) What is the probability that the sample has a mean of 61 or less inches?
probability =  

b) What is the probability that the sample has a mean between 68 and 71 inches?
probability =  

Note: Do NOT input probability responses as percentages; e.g., do NOT input 0.9194 as 91.94.