A table tennis match is played between Jack and Rose. The winner of the match is the one who first wins 4 games in total, and in any game the winner is the one who first scores 11 points. Note that in an individual game, if the score is 10 to 10, the game goes into extra play (called deuce) until one player has gained a lead of 2 points. Let p be the probability that Rose wins a point in any single round of serve, and assume that different rounds in all games are independent. (i) How many games can there be at most before a match winner appears? (ii) In a given individual game, what is the probability that the game runs into the deuce stage? (iii) Suppose that p = 0.6. Compute the probability that Rose wins the match? (iv) As a function of p, let F(p) be the probability that the match ends with a maximal number of games. For what value(s) of p is F(p) largest? Justify your answer and compute the resulting probability.

State University employs a large number of graduate students to work as teaching assistants. The teaching assistants often complain about their work. They feel that faculty and administrators demand too much. A common complaint is their low wages. The graduate students frequently point out that they do much the same work as faculty members, yet they receive only a very small percentage of the pay that faculty members receive. They also claim that faculty members frequently treat them unfairly. Teaching assistants are often asked to do large amounts of grading in very short time periods. Many also feel that faculty members are not very good at communicating expectations.

In response to the dissatisfaction of the teaching assistants, a local union representing public workers has begun efforts to organize a labor union. Union representatives have obtained campaign card signatures from 40 percent of the teaching assistants. An election is scheduled for next month. Union representatives have been busy making a case that the union can help ensure that teaching assistants are treated more fairly. They have publicized statistics showing that unionized workers make significantly more than nonunionized workers. University administrators have decided not to actively oppose union organization. They have simply stated that it is important for teaching assistants to have the opportunity to decide whether they should be represented by a labor union.

Some faculty members are sympathetic to the concerns voiced by graduate students. They publicly state their concern that wages are too low. They also express frustration when they see some of their colleagues take advantage of students by assigning them large amounts of work to complete in short time periods. Other faculty members are less sympathetic. These professors talk about how they were treated even worse when they were graduate assistants. They seem to find joy in looking back and telling war stories about “the old days.” They seem to think that working hard for little pay is a right of passage that helps prepare students for future careers. Overall, the faculty at State University thus seems to be about evenly split in their support for student efforts to unionize.

A majority of the undergraduate students at State University don't seem to know anything about the unionization efforts. A few politically active students have joined public rallies supporting the unionization efforts. Others seem to have used the unionization issue to complain about the quality of teaching provided by graduate students. These students recently met with administrators to complain about having too many graduate students as instructors. Just last week the local newspaper printed an article detailing some of the problems experienced when courses are taught by graduate students.

As a community, State University thus seems to be quite divided over the unionization issue. No matter who prevails in the election, it seems likely that a large number of people will be unhappy with the result.

Question:

Do you think a union would help resolve the complaints of the teaching assistants?

What makes the position of teaching assistant different from many jobs frequently represented by unions?

Do you think the administration's response is appropriate?

If you were a graduate student at State University, would you vote for the union? Why?

If exports increased to Canada and imports from Canada to the US also increased, without any other changes in the US and Canada's economies, then what would happen to the US Dollar exchange rate to the Canadian Dollar? Explain. Justify your answer.

suppose the 2000 US census is collected for every person in the US and it allows researchers to calculate summary quantities like the percent of the US population in a specified age range. What is the mean squared error of these summary quantities calculated from the census?

For the Spirit God gave us does not make us timid, but gives us power, love, and self discipline ~ Timothy 1:7

What do you hope to gain from this course PSY 560 Learning, Cognition, and Motivation

How does sport governance in the US differ from governance in other countries? Would a ministry of sport benefit the US?

Identify some challenges a Chinese investor may encounter in the US.

Are these challenges different from those facing a US investor?

Your comment to each question has to be more than five(5) sentences based on researched facts and logical analysis to earn the full credit.

Global outsourcing, is it good, bad or ugly?

In the recent years, we often heard about global outsourcing in US business.

Especially, when US economy was sluggish, one of major blames went for Global outsourcing, due to US job loss to overseas.

Q1) Global outsourcing, is it bad? because US manufacturing jobs went to China or India at the expense of US labors.

Q2)Global outsourcing, is it good? because US business can take an advantage of cheaper foreign labors to survive like an introduction of new technology such as robot or computer or can attract insourcing from overseas.

Q3) Global outsourcing, is it ugly? because US business can exploit the sweat shops from overseas.

Q4) Global outsourcing, is it inevitable like new technology? The robot with artificial intelligence could replace human labors in the future.

Q5) Give us your personal verdict over Global outsourcing. Also do you think which direction of trade policy is better for the economic welfare of US as well as the rest of the world; one US policy makers continue to move US toward more open and global economy by promoting trade, or one US policy makers move US toward more closed and isolated economy by protecting US industries?