In Country A, the income tax rate is 30%.

John, who is a resident of Country A, earns 10 a year, is going to report his income.

(A) If he underreports his income, it is detected with 10% probability and the penalty is
the square of the underreported income. (If he reports 8 and is detected, he should pay
2² = 4 as penalty.) If John is risk neutral, how much income is he going to report?

(B) The tax office can increase the detection probability to 20% with the cost of x. Compare
the expected tax revenue and penalty income of the tax office. For which range of x, is
it beneficial for the tax office to increase the detection probability?

(C) Suppose the detection probability of underreporting is increasing with the amount of underreporting.

The detection probability is given as 10% + 10% x M, where M is the amount of underreporting.

The penalty, once detected, is the same as the amount of underreporting. If John is risk neutral, how much income is he going to report?

The weights of a certain brand of candies are normally distributed with a mean weight of0.8612g and a standard deviation of 0.0514g. A sample of these candies came from a package containing 452 candies, and the package label stated that the net weight is 385.9g.​ (If every package has452candies, the mean weight of the candies must exceed 385.9 Over 452 =0.8538g for the net contents to weigh at least 385.9

​g.)a. If 1 candy is randomly​ selected, find the probability that it weighs more than

0.8538

g.The probability is

​(Round to four decimal places as​ needed.)

b. If 452candies are randomly​ selected, find the probability that their mean weight is at least 0.8538g.The probability that a sample of

452candies will have a mean of 0.8538g or greater is

(Round to four decimal places as​ needed.)

c. Given these​ results, does it seem that the candy company is providing consumers with the amount claimed on the​ label?

▼

No,

Yes,

because the probability of getting a sample mean of

0.8538

g or greater when

452

candies are selected

▼

is not

is

exceptionall small

The Transportation Safety Authority (TSA) has developed a new test to detect large amounts of liquid in luggage bags. Based on many test runs, the TSA determines that if a bag does contain large amounts of liquid, there is a probability of 0.9 the test will detect it. If a bag does not contain large amounts of liquid, there is a 0.09 probability the test will conclude that it does (a false positive). Suppose that in reality only 1 in 100 bags actually contain large amounts of liquid.

a. What is the probability a randomly selected bag will have a positive test? Give your answer to four decimal places.

b. Given a randomly selected bag has a positive test, what is the probability it actually contains a large amount of liquid? Give your answer to four decimal places.

c. Given a randomly selected bag has a positive test, what is the probability it does not contain a large amount of liquid? Give your answer to four decimal places.

True or False:

a.) In a statistical study, the random variable X = 1, if the house is colonial and X = 0 if the house is not colonial, then it can be stated that the random variable is continuous.

b.) For a continuous distribution, P(X ≤ 10) is the same as P(X<10).

c.) For a continuous distribution, the exact probability of any particular value is always zero.

d.) For a binomial probability experiment, with n = 60 and p =.2, it is appropriate to use the normal approximation to the binomial distribution without continuity correction.

e.) All continuous random variables are normally distributed.

f.) In a binomial distribution the random variable X is discrete.

g.) Events that have no sample space outcomes in common and, therefore cannot occur simultaneously are referred to as mutually independent events.

h.) The probability of an event is the product of the probabilities of the sample space outcomes that correspond to the event.

i.) A classical probability measure is a probability assessment that is based on relative frequency.

Problem 16-05 (Algorithmic)

A major traffic problem in the Greater Cincinnati area involves traffic attempting to cross the Ohio River from Cincinnati to Kentucky using Interstate 75. Let us assume that the probability of no traffic delay in one period, given no traffic delay in the preceding period, is 0.8 and that the probability of finding a traffic delay in one period, given a delay in the preceding period, is 0.65. Traffic is classified as having either a delay or a no-delay state, and the period considered is 30 minutes.

1. Assume that you are a motorist entering the traffic system and receive a radio report of a traffic delay. What is the probability that for the next 60 minutes (two time periods) the system will be in the delay state? Note that this result is the probability of being in the delay state for two consecutive periods. If required, round your answer to three decimal places.
   
   =0.4225
2. What is the probability that in the long run the traffic will not be in the delay state? If required, round your answers to three decimal places.

Consider a one-dimensional random walker (using numpy) that can move every second. With probability pl = 1/3 it moves to the left, with probability pr = 1/3 it moves to right, and with probability pr = 1/3 it rests and does not move. Assuming at time t = 0, the random walker is at x = 0, plot (using matplotlib) the probability density function and the cumulative probability function for t = 10, t = 100, and t = 1000 seconds. Make just two plots; each showing all three time points. Remember that you need to simulate random walks many times to get good statistics. Make the same two plots for pl = 0, pr = 1/2, and pr = 1/2. Do you understand why these plots look different? The plots that you make should be designed well. For example, they should label curves, axes, etc. (USING PYTHON)

2. We are interested in analyzing data related to the Olympics from one decade. We are looking at individuals and if they participated in the summer or winter Olympics and whether or not they won a medal. Use S to denote summer and M to denote if a medal was won. The probability that someone participated in the summer Olympics is 72%. The probability that they won a medal is 13%. The probability that they won a medal and it was in the summer Olympics is 10%. ( please show steps)

a. What percentage of people participated in the summer Olympics or won a medal?

b. What percentage of people participated in the winter Olympics?

c. Given someone won a medal, what is the probability that they participated in the summer Olympics?

d. What percentage of people did NOT participate in the summer games NOR won a medal?

e. Are M and S mutually exclusive events? Why or why not? f. Are M and S independent events? Explain, using probabilities.

g. If we know someone participated in the summer Olympics, what is the probability that they also won a medal?

1. For each set of atoms/ions, write them in increasing order of size (smallest to largest) a. Mg2+, Se2- , S2- , K+ , Ca2+ b. Ga, Si, Rb, N, In c. A2+, B+ , C, D- , E2- if these elements are isoelectronic (same number of electrons) d. Put the following elements, S, Ba, Bi, Cl, Te, Ar in order of increasing ionization energy, and increasing electron affinity.

2. The following questions involve the following atoms: Ge, As, K, N, O a. Draw the Lewis symbol for each atom b. Put the atoms in order of increasing electronegativity c. If any two atoms in the above list could be paired to make a bond, which two would lead to the most polar bond?

3. Calculate the lattice energy of MgCl2: MgCl2(s)Mg2+ (g) + 2Cl- (g) given the following: The sum of the 1st and 2nd ionization energy required to make Mg2+ is 2189 kJ/mol The heat of formation of Cl(g) is 121 kJ/mol The heat of formation of MgCl2 is -641.6 kJ/mol The electron affinity of Cl(g) is -349 kJ/mol The heat of formation of Mg(g) is 147.1 kJ/mol

4. Out of the following ionic compounds LiCl, Li2O, Na2S, BeF2, Al2S3, CaS a. Put them in order of increasing bond distance between the cation/anion, lowest to highest (Li-O distance in the formula unit Li2O). Use Figure 7.8 from text. b. Put them in order of increasing (lowest to highest) lattice energy

5. Draw Lewis structures (octet rule) for the following molecules: HCN, SF3 + , CH2Cl2, ClF3, BO3 3- , CH2CCl2 (the two carbon atoms are bonded to each other), CH3OH. If a double or triple bond is required, state your reasoning as to why you came to that conclusion.

6. Two Lewis structures for BF3 are given below. Determine the formal charge for each atom (write the formal charge next to the atom) in both structures and identify the correct structure. Redraw these structures on your homework.

7. Incorrect Lewis dot structures for PCl3 and CCl2O are given below. Disregarding any resonance considerations, identify the mistakes (explicitly state the mistake) in the list of instructions that led to the drawing of these incorrect structures.

Bookstore Sale The SOU’s bookstore is having a student appreciation sale. Students will receive a discount on all nontextbook items, depending on the total spent on those items. Discounts will be applied as follows:

$0 - $50.99 4%

$51.00 - $60.99 5%

$61.00 - $70.99 6%

$71.00 – $80.99 7%

$81.00 – $90.99 8%

$91.00 – $100.99 9%

$101.00 or more 10%

Regular prices

Book Bags $40

Sweatshirts $20

Magazines $3

Notebooks $2

Candy $1

Spreadsheet will show the sales for three students. The regular prices will be placed in a table at the top of the sheet, along with today’s date and your name. (Make the date static so it won’t update when the spreadsheet is opened later.) The volume discount will be placed in a second table. You will make a table showing how many of each item the student has purchased (you will make up the number of items). Calculate the total for the sale (must use SUMPRODUCT), and then use a VLOOKUP function to determine the percentage discount. The percentage needs to display the dollar amount and not the discount percentage. Apply this percentage to the total to determine the discount amount in dollars. Subtract the discount price from the regular price to calculate the total sale. Try different purchases with different total amounts. Check to make sure that the correct discount is calculated for each sale. The bookstore manager is also interested in the total, average, largest, and smallest sale totals. Use currency format with two decimal places for the all dollar amounts and percent format with 0 decimal places for the percentage amounts. Make formatting changes to improve the look of the spreadsheet (enhancements), add clipart or picture to your worksheet and submit finished worksheet in Moodle. If you use a table, be sure to convert the table back to a normal range before submission.

student 1 student 2 student 3

I need help with the following equations

An insurance company believes that people can be divided into two classes: those who are accident prone and those who are not. Their statistics show that an accident prone person will have an accident within a year with a probability of 0.4, whereas the probability for a nonaccident prone person is 0.2. It is assumed that 30% of the population is accident prone. Given that a new policyholder has an accident within a year of purchasing a policy, what is the probability that he or she is accident prone?