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Problem Set 01:

The network for this task has two input nodes, one hidden layer consisting of two nodes, and one output node. It uses a ReLU activation

function. For the hidden layer, the weights for the first hidden node (from the input nodes) are (2.3, -0.64, 2). The last number is the

weight for the bias term. The weights for the second hidden node are (-3, -2, -1).

For the output layer, the weights are (5, 3, -34).

Calculate the output for the following inputs (where the bias term is the last value of each vector). Show your work.

1. (-4, -2, 1)

2. (0, -2, 1)

3. (4, -2, 1)

4. (0, -3, 1)

1. If a firm moves from one point on a production isoquant to another point on the same isoquant, which of the following will certainly not happen?

options:

1-) A change in the level of output

2-) A change in the marginal products of the inputs

3-) A change in the rate of technical substitution

4-) A change in profitability

5-) All of these.

2. When Farmer Bob applies N pounds of fertilizer per acre, the marginal product of fertilizer is 1 − [1/N] bushels of corn. If the price of corn is $1 per bushel and the price of fertilizer is $0.75 per pound, then how many pounds of fertilizer per acre should Farmer Bob use in order to maximize his profits?

1-) 12

2-) 25

3-) 50

4-) 75

5-) None of these are correct.

3.A profit maximizing monopolist sets:

1-) average cost equal to price

2-) marginal cost equal to price

3-) price equal to marginal revenue

4-) marginal cost equal to marginal revenue

4. If the production function is f(L, K) = aL +2aK where a > 0 is a constant, L is for Labor and K is for Kapital, then the ratio of Marginal Product of Labor to Marginal Product of Capital is:

1-) 1/2

2-) 1

3-) 5

4-) 2

None of these are correct.

How to write a C++ of CountingSort function using 2D vector?

CountingSort(vector > array)

Input
# of rows: 2
Input Row 1: 9 8 7 6 3 2 1 5 4

Input Row 2: 1 2 4 3 5 6 9 8 7

Output

1,2,3,4,5,6,7,8,9

1,2,3,4,5,6,7,8,9

Suppose that the current 1-year rate (1-year spot rate) and expected 1-year T-bill rates over the following three years (i.e., years 2, 3, and 4, respectively) are as follows:

₁R₁ = 3.26%, E(₂r₁) = 4.70%, E(₃r₁) = 5.20%, E(₄r₁) = 6.70%

Using the unbiased expectations theory, calculate the current (long-term) rates for 1-, 2-, 3-, and 4-year-maturity Treasury securities. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

1

2

3

4

3.50

Passedix is a game of chance played with three fair dice. Players bet whether the sum of the faces shown on the dice will be above or below ten. During the late sixteenth century, the astronomer and mathematician Galileo Galilei was asked by the Grand Duke of Tuscany to explain why “the chance of throwing a 9 with three fair dice was less than that of throwing a 10.” (Interstat, Jan. 2004) The grand duke believed that the chance should be the same because “there are an equal number of partitions of the numbers 9 and 10.” Find the flaw in the Grand Duke’s reasoning and answer the question posed to Galileo. Hint: What the Grand Duke was saying is: There are six ways to get a 9: 1+2+6; 1+3+5; 1+4+4; 2+2+5; 2+3+4; 3+3+3. There are also six ways to get a 10: 1+3+6; 1+4+5; 2+2+6; 2+3+5; 2+4+4; 3+3+4. [10 pts] 3.56 Two fair dice are tossed, and the following events are defined: A: {Sum of the numbers showing is odd} B: {Sum of the numbers showing is 9, 11, or 12} Are events A and B independent? Why? [10 pts]

Top Billers processes invoices for business clients. Lately, Top Billers has been getting complaints about errors in the invoices they have processed. The quality manager for Top Billers decides to select one client at random each day and sample all of that client’s invoices to measure the extent of the problem.

a)   If the manager decides to construct a u-chart, what values will be used for the center line, lower control limit, and the minimum and maximum values of the upper control limit of the control chart?

b)   Create the control chart.

c)   Does the process appear to be in statistical control? Why or why not?

d)   What conclusion can be drawn about the overall quality of the service Top Billers offers?

Use the following information to answer problems 1 through 5: Han Solo guesses randomly at

six multiple choice questions on an exam. Each question has four potential answers.

Page

2

of

2

7. This scenario can be modeled as a

(a) normal experiment with 4 trials and success probability of 1/6 per trial.

(b) normal experiment with 6 trials and success probability of 1/4 per trial.

(c) binomial experiment with 6 trials and success probability of 1/5 per trial.

(d) binomial experiment with 4 trials and success probability of 1/6 per trial.

(e) binomial experiment with 6 trials and success probability of 1/4 per trial.

8. Complete the following table that represents the probability distribution of

X

= the number of

questions Han guesses correctly.

x

0

1

2

3

4

5

6

P(X = x)

(a) 1/7, 2/7, 3/7, 4/7, 5/7, 6/7, 1

(b) .1780, .5339, .8306, .9624, .9954, .9996, 1

(c) 1/7, 1/7, 1/7, 1/7, 1/7, 1/7, 1/7

(d) .1780, .3560, .2966, .1318, .0330, .0044, .0002

(e) 1/6, 1/6, 1/6, 1/6, 1/6, 1/6

9. What is the probability he will answer at least 4 of the questions correctly?

(a) 0.0376 (b) 10/12 (c) .67% (d) 2/12 (e) 0.0046

10. What is the mean number of questions he will answer correctly?

(a) 0 (b) 1 (c) 1.5 (d) 2 (e) 4

11. What is the standard deviation of the number of questions he will answer correctly?

(a) 0.46 (b) 1 (c) 1.06 (d) 1.5 (e) 1.6

In a study of cereal leaf beetle damage on oats, researchers measured the number of beetle larvae per stem in small plots of oats after randomly applying one of two treatments: no pesticide or Malathion at the rate of 0.25 pound per acre.

Is there significant evidence at the 1% level that the mean number of larvae per stem is reduced by Malathion? Carry out a complete test.

In a study of cereal leaf beetle damage on oats, researchers measured the number of beetle larvae per stem in small plots of oats after randomly applying one of two treatments: no pesticide or Malathion at the rate of 0.25 pound per acre.

Is there significant evidence at the 1% level that the mean number of larvae per stem is reduced by Malathion? Carry out a complete test.

During what part of interphase are the chromosomes replicated?

Question A options:

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Question B (1 point)

What is the name of the area (2) that the two copies of chromatids remain attached in a chromosome?

Question B options:

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Question C (2 points)

Match the four phases of mitosis with the characteristic on the right that best describes its phase, or a part of its phase.

Question C options:

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Question D (1 point)

In humans, the cells that are generated at the end of meiosis (both I and II) are called:

Question D options:

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Question E (2 points)

Question E options:

Male gametes are called

and female gametes are called

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Question F (2 points)

Choose all of the correct statements below that pertain to homologous chromosomes:

Question F options:

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Question G (1 point)

At the end of meiosis I and II, there are:

Question G options: