Suppose a coin is biased. Specifically, the probability that the flip shows as heads is a random variable P with the probability density function f P(p) = 2(1−p) for 0 ≤ p ≤ 1. Let N be the number of heads in n independent flips of the coin. Find E [ N ] using iterated expectation.

Meredith Shomers manages scholarship endowments for a major public university. Presently, she is trying to determine how much scholarship money may be awarded from an endowment with a current balance of $538,000. The endowment’s funds are invested in a portfolio whose annual return varies and may be represented as a normally distributed random variable with a mean of 6% and standard deviation of 2%. The legal terms of the endowment require Meredith to determine a constant scholarship payment amount from the endowment that, if made in each of the next 10 years, would result in only 5% chance of the endowment’s ending value drop- ping below its current value. Assume scholarship payments are withdrawn from the fund at the end of each year.
a. Create a spreadsheet model for this problem.

b. What is the maximum scholarship payment that should be made in the current
year?

A submarine can use sonar (sound traveling through water) to determine its distance from other objects. The time between the emission of a sound pulse (a "ping") and the detection of its echo can be used to determine such distances. Alternatively, by measuring the time between successive echo receptions of a regularly timed set of pings, the submarine's speed may be determined by comparing the time between pings. Assume you are the sonar operator in a submarine traveling at a constant velocity underwater. Your boat is in the eastern Mediterranean Sea, where the speed of sound is known to be 1522 m/s. If you sent out pings every 4.1 s, and your apparatus receives echoes reflected from an undersea cliff every 4.09 s, how fast is your submarine approaching the cliff?

Increased inequality in the distribution of income contributes to

A) The same percentage of income received by the highest and lowest quintiles of households

B) A smaller percentage of income received by the highest 20% of households

C) A greater percentage of income received by the highest 20% of households

D) A greater percentage of income received by the lowest 20% of households

Create a Java class named Trivia that contains three instance variables, question of type String that stores the question of the trivia, answer of type String that stores the answer to the question, and points of type integer that stores the points’ value between 1 and 3 based on the difficulty of the question.

Also create the following methods:

1. getQuestion( ) – it will return the question.
2. getAnswer( ) – it will return the answer.
3. getPoints( ) – it will return the point
4. setQuestion( String ) – sets the value of the question variable
5. setAnswer( String ) – sets the value of the answer variable
6. setPoints( int ) – sets the value of the points variable
7. Constructor to initialize the instance variables.
8. Overload Constructor to set the instance variables.
9. Add any other methods you need such as equal( ), toString( ), display( ), calcPoints( )...

Create Java application that contains a main method that plays a simple Trivia game. The game should have 5 questions. Each question has a corresponding answer and point value between 1 and 3. Implement the game using an array of 5 Trivia objects.

Next, open a binary file and store those 5 Trivia objects into a binary file then close the file. Open the file again to read each question one at a time and store them into an array of objects.

Randomly, display a question and allow the player to enter an answer.

If the player’s answer matches the actual answer, the player wins the number of points for that question. If the player’s answer is incorrect, the player wins no points for the question. Make sure the answer is not case sensitive and it is only one word or two words at most. The program should show the correct answer if the player is incorrect. After the player has answered all five questions, the game is over and your program should display the player’s total score.

Suppose we are interested in bidding on a piece of land and we know one other bidder is interested. The seller announced that the highest bid in excess of $15,000 will be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $15,000 and $20,000.

(a)

Suppose you bid $16,000. What is the probability that your bid will be accepted?

(b)

Suppose you bid $18,000. What is the probability that your bid will be accepted?

(c)

What amount should you bid in dollars to maximize the probability that you get the property?

$

(d)

Suppose you know someone who is willing to pay you $21,000 for the property.

What is the expected profit in dollars if you bid the amount given in part (c)?

$

Find a bid in dollars which produces a greater expected profit than bidding the amount given in part (c). (If an answer does not exist, enter DNE.)

$

Would you consider bidding less than the amount in part (c)? Why or why not?

Yes. There is a bid which gives a greater expected profit than the bid given in part (c), and thus a higher expected profit is possible with a bid smaller than the amount in part (c). No. The bid which maximizes the expected profit is the amount given in part (c), thus it does not make sense to place a smaller bid.    

I asked 100 students to complete a statistics test. the mean score on the test was 30 points with a standard deviation of 5 points. using this information and the normal distribution, calculate the following: [want to check my overall answers and help with the process of some] thank you

a. what is the probability a student earned a score of 45 points or less?

P(score <45 points)

i got 0.9987

b. what is the probability a student earned a score higher than 30 points?

P(score > 30 points)

not sure how to do this one

c. what is the probability a student earned a score between 25 and 45 points?

P(25 points < score < 45 points)

overall got 0.84.

d. i want to know the cutoff value for the upper 10%. what score separated the lower 90% of scores from the upper 10%?

P(score<____)=90% or 0.90 cumulative area to the left.

[i got p(score<0.8159)=90% --> x=34.0795 separates the scores.

e. want to know the cutoff values for the lowest 25% and the highest 25%

[not sure how to do these]

P(score<____)=25% or 0.25 cumulative area to the left.

P(score>____)=25% or 0.25 cumulative area to the right

In the accompanying​ table, the random variable x represents the number of televisions in a household in a certain country. Determine whether or not the table is a probability distribution. If it is a probability​ distribution, find its mean and standard deviation. LOADING... Click the icon to view the data. If the table is a probability​ distribution, what is its​ mean? Select the correct choice below and fill in any answer boxes within your choice. A. Its mean is nothing. ​(Round to the nearest tenth as​ needed.) B. The table is not a probability distribution. If the table is a probability​ distribution, what is its standard​ deviation? Select the correct choice below and fill in any answer boxes within your choice. A. Its standard deviation is nothing. ​(Round to the nearest tenth as​ needed.) B. The table is not a probability distribution.

in C programming language

Write a function removeDups that removes all duplicates in a given array of type int.

Sample Test Case:

• input -> {1,2,2,2,3,3,4,2,4,5,6,6}
• output -> {1,2,3,4,5,6,0,0,0,0,0,0}

More specifically, the algorithm should only keep the first occurance of each element in the array, in the order they appear. In order to keep the array at the same length, we will replace the removed elements with zeros, and move them to the end of the array.

2. (6 pts) Speculate on the effects of each of the following mutations on the translation of the following mRNA. Specifically indicate whether any product would be made, and if so, if it would be altered in any way.  (GpppG is the 5’ cap)

5’GpppGUAACAUGGUCGGACCAUGAC(A)₂₀₀3’

1. Mutation that removes the editing pocket from isoleucine-tRNA synthetase.

2. Mutation that prevents GTP hydrolysis of eEF1-a.

3. Mutation that prevents binding of GTP by eEF2.