In a box are six balls with the numbers 2, 6, 7, 13, 23, 34.

(a) (2 points) You draw four balls at the same time. What is the probability that two of them are prime numbers?

(b) (2 points) Draw a ball, put it back in the box, and draw another ball. Let A be the event that the first ball is even, and let B be the event that the product of the two numbers on the two balls is even. Are A and B independent?

(c) (2 points) Draw again two balls in the ways as in (b). Let X be the random variable assigning to the outcome the sum of the numbers on the two balls. What is P(X ≥ 50)? 1

(d) (2 points) Remove all balls from the box except 7 and 13. Draw again two balls from the box in the same way as (b) and let X be defined as in (c). Calculate its expected value.

1. A randomly selected freshman takes English with probability 0.7, takes Math with probability 0.5, and takes either English or Math with probability 0.8. What is the probability of taking both English and Math?

2. Two mutually exclusive events A and B have P(A) = 0.2, P(B) = 0.3. Find P (A or B).

3. Two independent events A and B have P(A) = 0.2, P(B) = 0.3. Find P (A or B).

4. If P (A | B) = 0.8 and P(B) = 0.6, find P (A and B).

5. Given the following table, evaluate

P(No), P (Woman and Yes), P (Man | Yes), P (No opinion | Woman), P(Men or No Opinion).

Are Women and No mutually exclusive?

Are Women and No independent?

6. A box contains 5 blue chips, 4 red chips, and 7 green chips. Select 10 chips at random.

1. In how many ways can this be done?
2. How many of these selections consist of 3 blue chips, 2 red chips, and 5 green chips?

(do not simplify your answers, leave them in terms of binomial coefficients).

A math teacher gave her class two tests. 40% of the class passed both tests and 80% of the class passed the first test. What percent of those who passed the first test also passed the second test (given the following formula for conditional probability)? Round your answer to the nearest whole percentage point.

P(B|A) = P(A and B) / P(A)

Select one:

a. 50%

b. 20%

c. 60%

d. 40%

q-2

Assume that you had a constraint satisfaction problem where you had the following set of numbers {1,2,3,4,5,6 } and you had to discover which numbers from the set could be added together to result in the sum of 7, which of the following would represent a breath first approach to building the search graph for solving this problem?

Select one:

a.

b.

c.

Q -3-----You go to see the doctor. The doctor selects you at random to have a blood test for swine flu, which for the purposes of this exercise we will say is currently suspected to affect 1 in 10,000. The test is 96% accurate, in the sense that the probability of a false positive is 4%. The probability of a false negative is zero. You test positive. What is the new probability that you have swine flu? (round to the nearest thousands place … 3 decimal places)

Two weeks ago LUML produced 300 light fixtures using eight employees. Each employee worked a standard week of 40 hours. Last week the company produced 240 standard fixtures using six employees who each worked 36 hours. In which period was productivity greater? Explain.

You will build some methods that search for the smallest element and the index of the smallest element in an array in a recursive fashion. I know you can already do this without recursion. The point is to use recursion, so use it.

public class Driver
{
   public static void main(String[] args)
   {
       int[] one = {2, 4, 6, 1, 6, 3, 8};
       int[] two = {43, 76, 3, 23, 95, 23};
       int[] three = {9, 8, 7, 6, 5, 4, 3, 2, 1};
       
       Recursion.print(one);
       System.out.println("Smallest: " + Recursion.smallest(one));
       System.out.println("Index of Smallest: " + Recursion.smallestIndex(one));
       System.out.println();
       
       Recursion.print(two);
       System.out.println("Smallest: " + Recursion.smallest(two));
       System.out.println("Index of Smallest: " + Recursion.smallestIndex(two));
       System.out.println();
       
       Recursion.print(three);
       System.out.println("Smallest: " + Recursion.smallest(three));
       System.out.println("Index of Smallest: " + Recursion.smallestIndex(three));
       System.out.println();
    }
}

public class Recursion
{
    public static void print(int[] array)
    {
        // Your code goes here.
    }
    
    public static int smallest(int[] array)
    {
        return smallestFrom(array, 0);
    }
    
    private static int smallestFrom(int[] array, int start)
    {
        // Your code goes here.
    }
    
    public static int smallestIndex(int[] array)
    {
        return smallestIndexFrom(array, 0);
    }
    
    private static int smallestIndexFrom(int[] array, int start)
    {
        // Your code goes here.
    }
}

Output

2,4,6,1,6,3,8
Smallest: 1
Index of Smallest: 3

43,76,3,23,95,23
Smallest: 3
Index of Smallest: 2

9,8,7,6,5,4,3,2,1
Smallest: 1
Index of Smallest: 8

Why are smallestFrom() and smallestIndexFrom() private? Should they be?

Why are all the methods in Recursion static? Could it be changed so they are not? Which one is better for this application?

match the words to the questions.

WORD BANK: precision, instrument precision, intra-assay precision, intermediate precision, interlaboratory precision, range, raw data, results, reagant blank, linear range, treated data, dynamic range, method blank, field blank, within-run precision, within-day precision, day-to-day precision, interoperator precision, interlaboratory precision.

The reproducibility of a result?

Also called injection precision, the producibility of an instrument reading when the same amount of one sample is introduced repeadetly?

The reproducibility of measurements on a unifrom material several times by one person on one day with the same equipment?

Also called ruggedness, the reproducibility of measurements by different people, on different days, on different places of equipment within the ame laboratory?

The reproducibilty of a measurement from the same sample by different people in different laboratories?

a blank sample containing all components except for analyte that has not been subjected to the steps of the chemical analysis?

concentration interval over which there is measurable response to a change in analyte concentration?

quantities reported upon completion of statistical analysis of the data?

a blank sample exposed to the environment at the sample collection site and transported in the same manner as other samples back to the lab?

individual measurements?

concentration interval over which the change in detector response is proportional to the analyte quantity?

concentration interval over which linearity, accuracy and precision meet specifications?

a blank sample containing all components except analyte that has been carried through all steps of the chemical analysis, including sample preparation?

amounts or concentrations determined by using a calibration method?

The reproducibility of measurements for the same sample during the course of a single run of an assay?

The reproducibility of an instrument reading during a single day, over several runs?

The reproducibility of measurements on a uniform material over several days?

The reproducibility of measurements by different people, on the same sample using the same method?

The reproducibility of a measurement from the same sample and method by different people in different laboratories?

New Brands Company is currently operating at 80 percent capacity. Worried about the company's performance, the general manager reviewed the company's operating performance. (All fixed costs are allocated costs.)

REQUIRED:

We have been using the same set of data (Data Set One) in the notes to illustrate production and costs. I have provided Data Set One in both tables below. When costs were calculated in the notes, fixed costs were $200. By using the term fixed costs economists are only referring to the fact that a firm must pay this expense no matter how much output it produces or sells. An example of a fixed cost could be the rent a small store pays on the space it rents. The rent will be the same for the duration of the lease, no matter if the store sells I item or 500 items. It is helpful to know what will happen to costs if the price of the variable or fixed resource changes.

PROBLEM ONE - Using the information in data set one, which I have included in the table below, recalculate total cost, fixed cost, variable cost, marginal cost, average total cost, average variable cost and average fixed costs if the price of the fixed input (the small stores rent) is not $200 but $220. A new lease may have caused the rent to increase. I have created Table 1 for you to put your answers in. Assume the price of the variable input, labor, is still $50 per unit. When fixed costs change which other costs will increase? Compare the costs you calculate for table one to the costs calculated in the notes in chapter 7 to find the answer.

TABLE ONE FOR ANSWERS TO PROBLEM ONE

Problem Two - Using the information in data set one, which I have included in the table below, recalculate total cost, fixed cost, variable cost, marginal cost, average total cost, average variable cost and average fixed costs if the price of the variable input (which is labor in this example) is not $50 but $55. I have created Table 2 for you to put your answers in. Assume that fixed costs remain at $220. When the price of a variable input changes which other costs will increase? Compare the costs you calculate for table two to the costs calculated in table one to find your answers.

TABLE TWO FOR ANSWERS TO PROBLEM TWO

International Asset Allocation: For this question assume that the world financial market is composed of only two economies, i.e., Canada and Japan. Also assume that the size of the Japanese market is TWICE that of the Canadian market. Each country has only two stocks. In Canada, we have BB and BELL and in Japan we have SONY and TOYOTA. Canadian optimal portfolio consists of 50% BB and 50% BELL, whereas Japanese optimal portfolio consists of 50% SONY and 50% TOYOTA. Suppose that Tom is a risk-averse investor. He has $100 to invest and he wants to invest 40% of his wealth in a risk-free asset and the rest in risky assets. If Tom uses the modern portfolio theory to allocate his investment, by how much he should invest in each of the risk assets, i.e., BB, BELL, SONY, TOYOTA.

I see theres solution posted but its done in Mathmatica format.

Can someone show me the solution using Matlab, please? Consider a particle in a room. How likely is the particle to hit the east wall of the room? Assume the western wall repels the particles and there is no vertical motion. The position at a subsequent time is related to the current position by x^n+1 = z^n + f(x^n) + Noise where f(x) = k/x^2 so that the force away from the western wall at x = 0 is proportional to the inverse of the distance squared. The noise is given by e times a random number between minus one and one. The eastern wall is taken to be at x = 5 and the constant of proportionality for the repulsive force is k = 0.5, with a noise amplitude of 1. Run at least 200 experiments and determine how many runs it took to reach the eastern wall. Plot the results.