Sole proprietorship
for 2019 what is the highest marginal income tax rate that an individual can pay?

1. Provide two reasons to why Prescriptive Analytics is considered the “highest level” of analytics? Illustrate with arguments.

There are 5 boxes. One box is empty; two boxes each contains one marble; and the remaining two boxes each contains two marbles. Suppose that the colors of the marbles are not known, but it is known that each marble can only be either red or green, with equal probability. Suppose that ONE box is randomly chosen from the 5 boxes, and let R denote the number of the red marble(s) the box has, and G be the number of the green marble(s) the box has. (Of course either R or G, or both, can be 0.)

(a) Write out the joint probability distribution of R and G.

(b) P(R > 0 ) = ?

(c) Write out the marginal distribution of G.

(d) P(G=1 | R=1) = ?

(e) E[R | G=1] = ?

(f) Are R and G independent? (Yes or no, you must justify your answer mathematically; otherwise, no credits can be given.)

(g) Calculate the correlation between R and G.

A typical deck of cards has 4 suits ( ♡,♢, ♡,♢, ♣,♠ ♣,♠ : and the following 13 denominations: Ace, 2 thru 10, Jack, Queen, and king). A full deck contains 52 cards. A single card has three characteristics: suit, denomination and colour. examples: [King of ♡ ♡ , is red] or [4 of ♣ ♣ , is black] etc.

(a) Say 4 cards are selected from the deck of 52, without replacement. Let X X be the number of ♢ ♢ 's drawn. What is the standard deviation of X,SD[X]=? (use at least four digits after the decimal point if rounding)

(b) If 30 cards are selected from the deck of 52, with replacement and you are also told the number of ♣ ♣ 's drawn is at most 10 but at least 3, what is the probability there will be exactly 6 ♣ ♣ 's drawn. Probability = equation editor (use at least four digits after the decimal point if rounding

Market-share-analysis company Net Applications monitors and reports on internet browser usage. According to Net Applications, in the summer of 2014, Google's Chrome browser exceeded a 20% market share for the first time, with a 20.37% share of the browser market.† For a randomly selected group of 15 Internet browser users, answer the following questions. (Round your answers to four decimal places.)

(a) Compute the probability that exactly 9 of the 15 Internet browser users use Chrome as their Internet browser. (Round your answer to four decimal places.)

(b) Compute the probability that at least 3 of the 15 Internet browser users use Chrome as their Internet browser. (Round your answer to four decimal places.)

(c) For the sample of 15 Internet browser users, compute the expected number of Chrome users.

(d) For the sample of 15 Internet browser users, compute the variance and standard deviation for the number of Chrome users. (Round your answers to four decimal places.)

variance =

standard deviation =

• According to the CDC, about 15% of adults who go to the doctor with a sore throat will have strep throat.
• If a patient does have strep throat, there is a 64.6% probability that the rapid strep test will give a positive test result. This number (64.6%) is called the sensitivity of the rapid strep test.
• If a patient does not have strep throat, there is a 96.8% probability that the rapid strep test will give a negative test result. This number (96.8% is called the specificity of the rapid strep test.

Using the information above, complete the following sentences:

We can conclude that out of every 100 people who test positive for strep throat using the rapid strep test, about _____% will not have strep throat and _______% will have strep throat.

We can conclude that out of every 100 people who test negative for strep throat using the rapid strep test, about _____% will not have strep throat and _______% will have strep throat.

Please show the calculations you used to get the answers! Thank you!

You would like to determine who in a group of 100 students carries antibodies for a certain virus. You can perform blood tests on each student individually, which would require 100 tests. Instead, you can partition the students into 10 groups of 10. Combine the blood samples of the 10 students in each group, and analyze the combined sample. If none of the 10 students in that group carries the antibodies, the test will show negative, while if one or more do carry the antibodies, the test will turn out positive, and you could then test every student in that group individually, resulting in a total of 11 tests for that group. If each person has the antibodies with probability .1, independently of each other,

find: (a) The maximum number of tests you may need to perform.

(b) The expected number of tests you’ll perform.

(c) Explain in words whether you would raise or lower the group sizes when the antibody probability is close to 0 or 1.

Homework Problem 13_1

Q13_1 Suppose the current spot rate of a one year bond YTM₁ =5% and the current spot rate of a two year bond YTM₂ =5.5%. The bond buyer wants an option to prepay the bond next year at $952.3810 (yield of 5%). In other words, he wants the option to put or sell the bond at $952.3810. Assume the bond yield can go to 8% with probability .5 or come down to 4% with probability .5.

a) The Replicating Portfolio is a portfolio of 1-yr and 2-yr bonds that exactly replicates the payoff of the put option under all conditions, in this case the two states.

What is this portfolio of one-year bonds (number of units of par, long/short) and two-year bonds (number of units of par, long/short) that has same payoff of this Put option?

b) What is the fair value of this Put? and why?

c) What is the yield of this bond?

d) What is the OAS of the bond if the market price is $910?

In the 1992 presidential election, Alaska's 40 election districts averaged 2026 votes per district for President Clinton. The standard deviation was 593. (There are only 40 election districts in Alaska.) The distribution of the votes per district for President Clinton was bell-shaped. Let X = number of votes for President Clinton for an election district. (Source: The World Almanac and Book of Facts) Round all answers except part e. to 4 decimal places.

a. What is the distribution of X? X ~ N(____,____)

b. Is 2026 a population mean or a sample mean?

c. Find the probability that a randomly selected district had fewer than 2046 votes for President Clinton. Show all work (including how to get z and how to convert from z table)

d. Find the probability that a randomly selected district had between 2202 and 2334 votes for President Clinton.

e. Find the third quartile for votes for President Clinton. Round your answer to the nearest whole number.