There is an study which contains 4 questions as follow:

I) 3 questions have four multiple choices a, b, c and d

II) only one question is true and false

Let \( X \) denotes the number of correct answers for part (I) and \( Y \) denotes the number of correct answers in true/false part. Find the joint probability distribution function \( f_X,_Y(x,y) \)

Stephan makes 19 out of 25 foul shots. Use the normal distribution in probability and confidence interval calculations.

1. a) What is the a value for a confidence level of 80%?

2. b) What is the standard deviation of the sample proportion x/n where x is the number

   of made shots and n is the total number of shots?

3. c) What is the 80% confidence interval for underlying average foul shot percentage?

Suppose the probability of an IRS audit is 2.9 percent for U.S. taxpayers who file form 1040 and who earned $100,000 or more.

(a) What are the odds that such a taxpayer will be audited? (Round your answers to the nearest whole number.)
  
Odds that a taxpayer will be audited            to

(b) What are the odds against such a taxpayer being audited? (Round your answers to the nearest whole number.)
  
Odds against a taxpayer being audited      

You want to evaluate three mutual funds using the Jensen measure for performance evaluation. The risk-free return during the sample period is 6%, and the average return on the market portfolio is 18%. The average returns, standard deviations, and betas for the three funds are given below.

The fund with the highest Jensen measure is

Multiple Choice

• Fund A.

• Fund B.

• Fund C.

• Funds A and B (tied for highest).

• Funds A and C (tied for highest).

We are creating a new card game with a new deck. Unlike the normal deck that has 13 ranks (Ace through King) and 4 Suits (hearts, diamonds, spades, and clubs), our deck will be made up of the following.

Each card will have:
i) One rank from 1 to 16.
ii) One of 5 different suits.

Hence, there are 80 cards in the deck with 16 ranks for each of the 5 different suits, and none of the cards will be face cards! So, a card rank 11 would just have an 11 on it. Hence, there is no discussion of "royal" anything since there won't be any cards that are "royalty" like King or Queen, and no face cards!

The game is played by dealing each player 5 cards from the deck. Our goal is to determine which hands would beat other hands using probability. Obviously the hands that are harder to get (i.e. are more rare) should beat hands that are easier to get.

e) How many different ways are there to get exactly 3 of a kind (i.e. 3 cards with the same rank)?
The number of ways of getting exactly 3 of a kind is
DO NOT USE ANY COMMAS

What is the probability of being dealt exactly 3 of a kind?
Round your answer to 7 decimal places.

f) How many different ways are there to get exactly 4 of a kind (i.e. 4 cards with the same rank)?
The number of ways of getting exactly 4 of a kind is
DO NOT USE ANY COMMAS

What is the probability of being dealt exactly 4 of a kind?
Round your answer to 7 decimal places.

g) How many different ways are there to get a full house (i.e. 3 of a kind and a pair, but not all 5 cards the same rank)?
The number of ways of getting a full house is
DO NOT USE ANY COMMAS

What is the probability of being dealt a full house?
Round your answer to 7 decimal places.


h) How many different ways are there to get a straight flush (cards go in consecutive order like 4, 5, 6, 7, 8 and all have the same suit. Also, we are assuming there is no wrapping, so you cannot have the ranks be 14, 15, 16, 1, 2)?
The number of ways of getting a straight flush is
DO NOT USE ANY COMMAS

What is the probability of being dealt a straight flush?
Round your answer to 7 decimal places.


i) How many different ways are there to get a flush (all cards have the same suit, but they don't form a straight)?
Hint: Find all flush hands and then just subtract the number of straight flushes from your calculation above.
The number of ways of getting a flush that is not a straight flush is
DO NOT USE ANY COMMAS

What is the probability of being dealt a flush that is not a straight flush?
Round your answer to 7 decimal places.


j) How many different ways are there to get a straight that is not a straight flush (again, a straight flush has cards that go in consecutive order like 4, 5, 6, 7, 8 and all have the same suit. Also, we are assuming there is no wrapping, so you cannot have the ranks be 14, 15, 16, 1, 2)?
Hint: Find all possible straights and then just subtract the number of straight flushes from your calculation above.
The number of ways of getting a straight that is not a straight flush is
DO NOT USE ANY COMMAS

What is the probability of being dealt a straight that is not a straight flush?
Round your answer to 7 decimal places.

The quarterly returns for a group of 74 mutual funds with a mean of 1.1​% and a standard deviation of 4.9​% can be modeled by a Normal model. Based on the model ​N(0.011​,0.049​), what are the cutoff values for the ​a) highest 20% of these​ funds? ​b) lowest 40%? ​c) middle 80​%? ​d) highest 60%?

The quarterly returns for a group of 53 mutual funds with a mean of 2.1​% and a standard deviation of 5.1​% can be modeled by a Normal model. Based on the model ​N(0.021​,0.051​), what are the cutoff values for the ​

a) highest 10​% of these​ funds? ​
b) lowest 20​%?
​c) middle 40​%?
​d) highest 80​%?

An analysis of the results of a football team reveals that whether it will win its
next game or not depends on the results of the previous two games. If it won its
last and last-but-one game, then it will win the next game with probability 0.6; if
it won last-but-one but not last game, it will win the next game with probability
0.8; if it did not win the last-but-one game, but won the last one, it will win the
next game with probability 0.4; if it did not win the last-but-one nor the last game,
it will win the next game with probability 0.2. The dynamics of consecutive pairs
of results for the team follows a discrete time Markov chain with state space S =
{(W, W), (L, W), (W, L), (L, L)}, where W and L means the team won and lost
respectively. To simplify the notation put 1 ≡ (W, W), 2 ≡ (L, W), 3 ≡ (W, L) and
4 ≡ (L, L), so that the state space becomes S = {1, 2, 3, 4}.
i. Write down the transition probability matrix for the chain.
ii. Find the mean number of consecutive games the team won

An analysis of the results of a football team reveals that whether it will win its
next game or not depends on the results of the previous two games. If it won its
last and last-but-one game, then it will win the next game with probability 0.6; if
it won last-but-one but not last game, it will win the next game with probability
0.8; if it did not win the last-but-one game, but won the last one, it will win the
next game with probability 0.4; if it did not win the last-but-one nor the last game,
it will win the next game with probability 0.2. The dynamics of consecutive pairs
of results for the team follows a discrete time Markov chain with state space S =
{(W, W), (L, W), (W, L), (L, L)}, where W and L means the team won and lost
respectively. To simplify the notation put 1 ≡ (W, W), 2 ≡ (L, W), 3 ≡ (W, L) and
4 ≡ (L, L), so that the state space becomes S = {1, 2, 3, 4}.
i. Write down the transition probability matrix for the chain.
ii. Find the mean number of consecutive games the team won

In Java...

Create a class named _MyArrays which has a main( ) and other static methods.

Part I (30%) [Main method] In the main() - Request the number of reviewers (r) and movies (m) - Declare a r x m two-dimensional array of integers - Allow the user to enter distinct values , row by row to fill the two dimensional array - Display the two-dimensional array using a _displayArray method. - Using the _printHighestLowestMovieRating method print the highest and lowest rating for each movie. - Using the _printAverageReviewerRating method print the average reviewer rating for each reviewer. - Test your program with the information in the example on the first page.

Part II (20%) [_displayArray] The _displayArray method must have the following specifications and functionality: o Only Takes the two-dimensional array as a formal parameter/argument o Displays the array data as a matrix (i.e. Rows and Columns) ( you know how to find the row and column without (r ) and (m) ) o Does not return any value.

Part III (20%) [_printHighestLowestReviewerRating] The _ printHighestLowestReviewerRating method must have the following specification and functionality: o Takes the two-dimensional array as a formal parameter/argument as well as r and m o Displays each reviewer code and the highest and lowest rating. o Sample output “Highest rating for review # 1 is 6 and Lowest is 2”

Part IV (20%) [_ printAverageMovieRating] The _ printAverageMovieRating method must have the following specification and functionality: o Takes the two-dimensional array as a formal parameter/argument as well as r and m o Displays each Movie code and the average Movie rating. o Sample output : “ The average rating of the movie #4 is 6.67“

Puzzle #4

Five friends each wrote a letter to Santa Claus, pleading for certain presents. What is the full

name of each letter-writer and how many presents did he or she ask for? Kids’ names: Danny,

Joelle, Leslie, Sylvia, and Yvonne. Last names: Croft, Dean, Mason, Palmer, and Willis. Number

of presents requested: 5, 6, 8, 9, and 10.

Clues:

1. Danny asked for one fewer present that the number on Yvonne’s list.

2. The child surnamed Dean asked for one more present than the number on the list written by

the child surnamed Palmer.

3. Sylvia’s list featured the fewest presents, and the letter written by the child surnamed Willis

featured the highest quantity.

4. Joelle asked for one fewer present than the number specified in the Croft child’s letter.

Make your grid to solve:

Croft

Dean Mason Palmer Willis

5

6

8

9

10

Danny

Joelle

Leslie

Sylvia

Yvonee

5 presents

6 presents

8 presents

9 presents

10 presents

Your final answers to puzzle 4: