Consider a murder trial. Two states of nature: θ1=”Guilty”, θ2 =”Innocent”. Two actions for the jury: a1 =”Jail”, a2 =”Free”. The loss function is zero if the jury makes a correct decision. The loss is 5 if the jury let’s a criminal free but it is 10 if an innocent person is sent to jail. Data from DNA is available in the form of a statistical variable X with X|θ1 ∼ N(1, 1/4) and X|θ2 ∼ N(0, 1). Find the Bayes rule under the assumption of equal a priori probabilities. The Bayes rule sends the accused to jail if and only if,

(A) 0 < x < 1

(B) x > 3 4

(C) 1 3 < x < 1

D) 2 3 < x < 2

(E) 1 < x < 2

In Python. A file concordance tracks the unique words in a file and their frequencies. Write a program that displays a concordance for a file. The program should output the unique words and their frequencies in alphabetical order. Variations are to track sequences of two words and their frequencies, or n words and their frequencies.

Below is an example file along with the program input and output:

Input : test.txt

output : 3/4 1, 98 1, AND 2, GUARANTEED 1, INDEED 1, PERCENT 1, SUCCEED 1, WILL 2, YES 1, YOU 2

The code needs to read different files by name and also the count the amount of times or occurrence the word showed up and attach the number to the word like above.. The text file will say  

"AND YOU WILL SUCCEED

YES

YES YOU WILL INDEED

98 AND 3/4 PERCENT"

) Find the following integral by using cylindrical coordinates

\int _0^4\int _{-\sqrt{16-y^2}}^{\sqrt{16-y^2}}\int _{-\sqrt{16-x^2-y^2}}^0\left(xy^2+6\right)\:dxdydz

1. TreeSetDemo

IN JAVA PLEASE

The following program can be done all in the main method. It demonstrates that a TreeSet eliminates duplicates and is ordered.

Create a Random object with a seed of 5.

Create an ArrayList numAL of type Integer

Populate numAL with 10 numbers randomly selected from 0 to 6

Print out numAL

Create a TreeSet numTS of type Integer

Create an Iterator alIter from numAl and use it to add all the elements of numAL in numTS.

Print out numTS

Sample output:

ArrayList: [2, 4, 4, 0, 4, 0, 1, 5, 5, 5]

TreeSet: [0, 1, 2, 4, 5]

1. Give a recursive algorithm to solve the following recursive function.

f(0) = 0;

   f(1) = 1;

  f(2) = 4;

f(n) = 2 f(n-1) - f(n-2) + 2; n > 2

b)

Solve f(n) as a function of n using the methodology used in class for Homogenous Equations. Must solve for the constants as well as the initial conditions are given.

Which factor is more than likely the reason for the rapid speed of action of injected drugs?

Question 16 options:

1)

How quickly the substance enters the bloodstream

2)

How quickly it reaches the site of action

3)

How much of the drug reaches the target site

4)

All of the above

Question 17 (1 point)
A new drug is being developed to treat acne. Scientists have found that a therapeutic does is about 150mg, and that an increase of 5mg is sufficient to cause bizarre skin rashes. This new drug has narrow:

Question 17 options:

1)

Site of action

2)

Potency to toxicity ratio

3)

Margin of safety

4)

Dose-response curve

Question 18 (1 point)
When a person is given a dose of 2mg of Ativan, it takes approximately 6 hours for 1mg of Ativan to leave the body. This refers to Ativan's

Question 18 options:

1)

Time to biotransformation

2)

Plateau effect

3)

Rate of metabolism

4)

Half life

Question 19 (1 point)
Gene has cirrhosis and when he takes Tylenol, he has a much different response to it than his wife. Which of the following is the most likely contributing factor to this difference in response?

Question 19 options:

1)

Body size

2)

Stomach contents

3)

Liver enzyme activity

4)

Health status

Given the following functions, can you have the corresponding a) Fourier series, b) Fourier transform and c) Laplace transform? If yes, find them, if not, explain why you can not.

A, x(t) = -1+cos(2t) + sin（pai*t+1)                                               (4-1)

B, x(t) = 2d(t) cos(2t) +d(t-1.5p) sin(2t)                                          (4-2)

C, x(t) = 1+cos(1.5t) + cos(4t)                                           (4-3)

Given the following functions, can you have the corresponding a) Fourier series, b) Fourier transform and c) Laplace transform? If yes, find them, if not, explain why you can not.

A, x(t) = -1+cos(2t) + sin(pt+1)                                                                                 (4-1)

B, x(t) =2d(t) cos(2t) +d(t-1.5p) sin(2t)                                                                    (4-2)

C, x(t) = 1+cos(1.5t) + cos(4t)                                                                                    (4-3)

Problem 8-06

Bonita Company is a multiproduct firm. Presented below is information concerning one of its products, the Hawkeye.

Calculate average-cost per unit. (Round answer to 4 decimal places, e.g. 2.7613.)

1) Average-cost per unit =___________________________________?

Compute cost of goods sold, assuming Bonita uses: (Round average cost per unit to 4 decimal places, e.g. 2.7631 and final answers to 0 decimal places, e.g. 6,548.)

2)

Please clearly state the step number next to the answers given, thank you!

A random sample of 12 supermarkets from Region 1 had mean sales of 72.4 with a standard deviation of 6.2. A random sample of 16 supermarkets from Region 2 had a mean sales of 78.3 with a standard deviation of 5.3. Does the test marketing reveal a difference in potential mean sales per market in Region 2? Let μ1 be the mean sales per market in Region 1 and μ2 be the mean sales per market in Region 2. Use a significance level of α=0.05 for the test. Assume that the population variances are not equal and that the two populations are normally distributed.

Step 1 of 4: State the null and alternative hypotheses for the test.
Step 2 of 4: Compute the value of the t test statistic. Round your answer to three decimal places.
Step 3 of 4: Determine the decision rule for rejecting the null hypothesis H0. Round your answer to three decimal places. (e.g. Reject H0 if t or |t| is < or > ___________)
Step 4 of 4: State the test's conclusion. (Reject or Fail to Reject)