Roulette is a casino game that involves spinning a ball on a wheel that is marked with numbered squares that are red, black, or green. Half of the numbers 1-36 are red and half are black, 0 and 00 are green. Each number occurs only once on the wheel.

The most common bets are to bet on a single number or to bet on a color (red or black). The pocket in which the ball lands on the wheel determines the winning number and color. The ball can land on only one color and number at a time.

We begin by placing a bet on a number between 1 and 36. This bet pays 36 to 1 in most casinos, which means we will be paid $36 for each $1 we bet on the winning number. If we lose, we simply lose whatever amount of money we bet.

Calculate the probability that we will win on a single spin of the wheel.

Calculate the probability that we will lose.

What is the expected value of a bet on a single number if we bet $1?

What is the expected value of a bet on a single number if we bet $5?

What is the expected value of a bet on a single number if we bet $10?

Can you explain your responses to the three expected value questions?

We decide that we can certainly increase our chances of winning if we bet on a color instead of a number. This bet pays even money in most casinos. This means that for each dollar we bet, we will win $1 for choosing the winning color. So, if we bet $5 and win, we would keep our $5 and win $5 more. If we lose, we lose whatever amount of money we bet, just as before.

What is the probability that we will win on a single spin?

If we bet $60 on the winning color, will we win more or less than if we bet $8 on the winning number?

What is the expected value of a $1 bet on red?

What is the expected value of a $5 bet on red?

What is the expected value of a $10 bet on red?

How does the expected value of betting on a number compare to the expected value of betting on a color?

Are casinos really gambling when we place a bet against them? Explain.

The color distribution of plain M&M’s varies by the factory in which they were made. The Hackettstown, New Jersey plant uses the following color distribution for plain M&M’s: 12.5% red, 25% orange, 12.5% yellow, 12.5% green, 25% blue, and 12.5% brown. Each piece of candy in a random sample of 100 plain M&M’s from the Hackettstown factory was classified according to color, and the results are listed below. Use a 0.05 significance level to test the claim that the Hackettstown factory color distribution is correct. Describe method used for calculating answer.

(a) Identify the appropriate hypothesis test and explain the reasons why it is appropriate for analyzing this data.

(b) Identify the null hypothesis and the alternative hypothesis.

(c) Determine the test statistic. (Round your answer to two decimal places)

(d) Determine the p-value. (Round your answer to two decimal places)

(e) Compare p-value and significance level ?. What decision should be made regarding the null hypothesis (e.g., reject or fail to reject) and why?

(f) Is there sufficient evidence to support the claim that the Hackettstown factory color distribution is correct? Justify your answer.

The color distribution of plain M&M’s varies by the factory in which they were made. The Hackettstown, New Jersey plant uses the following color distribution for plain M&M’s: 12.5% red, 25% orange, 12.5% yellow, 12.5% green, 25% blue, and 12.5% brown. Each piece of candy in a random sample of 100 plain M&M’s from the Hackettstown factory was classified according to color, and the results are listed below. Use a 0.05 significance level to test the claim that the Hackettstown factory color distribution is correct. Describe method used for calculating answer.

Color Red Orange Yellow Green Blue Brown

Number 11 28 20 9 20 12

(a) Identify the appropriate hypothesis test and explain the reasons why it is appropriate for analyzing this data.

(b) Identify the null hypothesis and the alternative hypothesis.

(c) Determine the test statistic. (Round your answer to two decimal places)

(d) Determine the p-value. (Round your answer to two decimal places)

(e) Compare p-value and significance level α. What decision should be made regarding the null hypothesis (e.g., reject or fail to reject) and why?

(f) Is there sufficient evidence to support the claim that the Hackettstown factory color distribution is correct? Justify your answer.

The objective of this assignment is to imagine that a majority of people in your country believe international trade harms their wages and jobs, and that your task is to change their minds. Create an original discussion post by responding to the topic below utilizing the knowledge you accumulate while in this course in a minimum of two paragraphs. You must use proper grammar, spelling, and punctuation. Any outside sources that you use to support your opinions should be appropriately cited within your posting. To begin, click reply below.

Discussion Topic

1. How would you go about educating people about the benefits of trade?
2. What are some of the international trade patterns that you might use to help convince people that it is the best method? Why?
3. How would you explain absolute advantage to help influence people to encourage trade?
4. What are your experiences with trading? What has been successful? What has gone wrong?

Q.2 Some state Governments around Australia have pursued policies to merge local government councils. Explain the economics rationale for these policies, use cost curves and related evidence to support your arguments.

Draw the red-black BST that results when you insert letters A through K int order into an initially empty tree, then describe what happens in general when trees are built by insertion of keys in ascending order. What about descending order?

The Federal Reserve has a variety of responsibilities and goals. Choose one of these responsibilities or goals and explain it in more detail (e.g. explain what it means to be a "lender of last resort"). Finally, give your opinion on whether the Federal Reserve should have that responsibility or goal, and whether their authority over that responsibility or goal should be expanded, diminished or remain as it is and explain why. Include a detailed and accurate application of one or more of the concepts regarding the federal reserve responsibilities and goals.

Straight wooden rod of mass 6.0 kg, uniform cross-section 7 cm², and constant density 700 kg has a very small mass 0.8 kg attached to its one end. The rod is partially submerged in water of density 990kg/m³.  While in equilibrium, the rod floats in a vertical position with large part of it submerged. The rod is then pushed down by distance y_max from equilibrium and released resulting in its oscillation neat the surface of teh water.

(Assuming no drag forces are acting in this situation) and taking g to be 9.8 m/s²

A) Use the first principles to demonstrate that such system can be treated as Simple Harmonic Oscillator. ( Paper solution!!!)

B) Find the rod's period of oscillations to the nearest thousandth of a second.

( Enter this value into the answer box without units).

In addition to entering your final numerical answer into the box, make sure that you write your solution neatly starting with the clear diagram and all variables on it.

Solve this problem in detail on paper. Please annotate your solution -- make short comments/ arguments for steps you are making.

Use the following information: n_1=35,x ̅_1=5,s_1=3,n_2=32,x ̅_2=7,s_2=5 Test whether the score variance for the first population is significantly different from that of the second population at the significant level α=0.05, to do so: State null and alternative hypotheses. Compute the test-value. Find the critical value. Make your decision and explain the reason. Use the result part (a) for assumption on variance of two populations, test whether the second population mean is greater the first one at the level α=0.05, to do so state, The list of assumptions. Null and alternative hypotheses. Compute the test-value. Find the critical value. Make your decision and explain the reason.