Suppose it’s the 1970’s and you’re on the show Let’s Make a Deal. The host, Monty Hall, would offer the “Big Deal” to a contestant at the end. In exchange for their current winnings, they would be able to choose one of three doors. Behind one of the doors is a very big prize that you would want (We will call this the “winning door”), and behind the other two doors is something you would not want. Whichever door you choose, there will always be at least one non-winning door that Monty Hall will then open and reveal that “It’s a good thing you didn’t choose that one!” (In the case you chose the winning door, the host would decide randomly which of the other two doors to open.) Then, Monty Hall will give you a decision to make: You may switch your choice to the other non-revealed door if you would like.

Now let "door A" be the name of the door you chose, and let the event A be that this is the winning door. Let B and C be the events that "door B" and "door C" are the winning doors, respectively. Which door the prize is placed behind is random, so your prior probabilities are P(A) = P(B) = P(C) =1/3. Also say "door B" is the name of whichever door that Monty Hall then decides to reveal. And let openB be the event that Monty hall revealed "door B".

(a) In a sentence or two for each, explain why P(openB|A) = 1/2, P(openB|B) = 0, and P(openB|C)= 1.

(b) Given the priors and the values from part a, use Bayes's Rule and the Law of Total Probability to calculate both P(A|openB) and P(C|openB)

(c) In a letter to The American Statistician in 1975 a version of the following problem was proposed and solved, and it a gained a considerable amount of fame after reappearing in a Parade Magazine column in 1990:

Do you want to keep door A, or do you want to switch to door C? Or does it not matter? Now that you have calculated the probabilities of the prize being behind these doors, explain which decision you would make.

How important is it for an individual to begin investing early for retirement? Do you think an individual should seek high-return investments when they are still relatively young?

Original response please

In early December, the Snowland Resort was paid $1,600 by a company to host its holiday party that month.

In addition to receiving the cash, the $1,600 is considered which of the following?

• Profit

• Expense

• Equity

• Revenue

For a number of reasons, economists believe that the natural rate of unemployment in the U.S. economy declined from the 1980s to the 1990s and early 2000s. Provide at least two different reasons for this phenomenon and discuss each.

Discuss the early history of photography from the sixteenth century to the Civil War with regard to specific photographers, inventors and photographic processes. Support your answer with examples from the text when possible.

1. EXPLAIN How nebulizer and inhaler assist in early detection of asthma symptom changes in children and teenagers?

2. Describe How NEBULIZER AND INHALER assist in THE disease management education OF ASTHMA?

1. why it is important to prioritize your research needs early in the process of conducting business research?

2. list 3 types of reports commonly used to monitor and control operations in the business.

What are the main reasons for the rapid expansion of the Asian middle class?

Why did Asia attract large capital inflows during the early-mid 1990s? Explain the impact on asset markets.

List five characteristics, in order from ancestral to derived that occurred during the eye development.

From early chordates' light sensitive pits to the current spherical evolved eye, in sharks for example.

What does John Graunt have to do with big data?

How is the Jacquard Loom related to computer programming?

What are some examples of early (pre 1930s) big data sets