Homework Set - Module 7

Suppose the large number of bike accidents in a small town results in new legislation that requires all citizens of the town to wear specialized bike helmets when riding. These new helmets reduce the probability of head trauma by 25% during a bike accident. While the new helmets    the probability of a serious head injury resulting from a bike accident, they also incentivize cyclists to ride    safely, which could    the number of bike accidents and thus head injuries to cyclists.

n people guess an integer between 1 and 100, and the winner is the player whose guess is closest to the mean of the guesses + 1 (ties broken randomly). Which of the following is an equilibrium: a) All announce 1. b) All announce 50. c) All announce 75. d) All announce 100

Now, imagine that Port Chester decides to crack down on motorists who park illegally by increasing the number of officers issuing parking tickets (thus, raising the probability of a ticket). If the cost of a ticket is $100, and the opportunity cost for the average driver of searching for parking is $12, which of the following probabilities would make the average person stop parking illegally? Assume that people will not park illegally if the expected value of doing so is negative. Check all that apply.

In a Godiva shop, 40% of the cookies are plain truffles, 20% are black truffles, 10% are cherry cookies, and 30% are a mix of all the others. Suppose you pick one at random from a prepacked bag that reflects this composition. a. What is the probability of picking a plain truffle? b. What is the probability of picking truffle of any kind? c. If you instead pick three cookies in a row, what is the probability that all three are black truffles?

Halsen, a marketing manager at Business X, has determined four possible strategies (X1, X2, X3, and X4) for promoting the Product X in London. She also knows that major competitor Product Y has 4 competitive actions (Y1, Y2, Y3 and Y4) it’s using to promote its product in London, too. Ms. Halsen has no previous knowledge that would allow her to determine probabilities of success of any of the four strategies. She formulates the matrix below to show the various Business X strategies and the resulting profit, depending on the competitive action used by Business Y. Determine which strategy Ms. Halsen should select using. Maximax, maximin or minimax regret?     Business X Strategy                Business Y Strategy     Y1 Y2 Y3 Y4 X1 25 57 21 26 X2 17 29 20 34 X3 47 31 32 37 X4 35 27 30 35

Halsen, a marketing manager at Business X, has determined four possible strategies (X1, X2, X3, and X4) for promoting the Product X in London. She also knows that major competitor Product Y has 4 competitive actions (Y1, Y2, Y3 and Y4) it’s using to promote its product in London, too. Ms. Halsen has no previous knowledge that would allow her to determine probabilities of success of any of the four strategies. She formulates the matrix below to show the various Business X strategies and the resulting profit, depending on the competitive action used by Business Y. Determine which strategy Ms. Halsen should select using, the following decision criteria. Please explain your answer for each strategy. a)Maximax;    b)Maximin;  c)Minimax regret      Business X Strategy                Business Y Strategy     Y1 Y2 Y3 Y4 X1 25 57 21 26 X2 17 29 20 34 X3 47 31 32 37 X4 35 27 30 35

A small bakery serves very popular fresh meat pies every day. The cost of making each pie is $2, and they are sold for $5 each. Unsold pies at the end of the day will be put for a quick sale for $1.00 each, and they are always sold out. The record of the past daily sales of the pies is presented below. Demand 100 150 200 250 300 350 Probability 10% 20% 25% 25% 15% 5% Answer the following question by showing the calculations: a. Construct a table of profits or losses for each possible quantity of the pies based on the demands as recorded above. How many pies should the bakery make every day to maximize the profit? b. Confirm your answer in sub-question a) using a full marginal analysis based on the costs of overestimating and underestimating demands.

2. (+3) For events A, B, and C, state whether each of the following is always true (T) or not always true (F): (a) P(A|B) + P(A|B) = 1 (b) If A and B are independent events then A is independent of B. (c) If P(C) > 0 and P(A) > P(B) then P(A|C) > P(B|C).

You are modeling a qualitative variable that takes on two classes (classes 1 and 2). In trying to classify observation 11 (out of 20) you compute the conditional probability for class 1 as 0.51. How would you classify this observation?

4. In a paper published in 2020, Robson and co-author Saul Schwartz, a professor in the School of Public Policy at Carleton, found that about 11% of Canadians don't file their tax returns.In our ECON224 class of 35 students: (a) What is the probability that at least 6 students won’t file their tax returns this year? (b) What is the probability that more than 30 students will file their tax returns this year? (c) What is the probability that the number of students in our ECON224 class who won’t file a tax return this year will be greater than 2 but less than 7? Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.

Using the random variables X and Y from Table 2.2, consider two new random variables W = 4 + 8X and V = 11 - 2Y. Compute (a) E(W) and E(V); (b) J2W and J2V; and (c) JWV and corr(W, V).

Ex 8. An airline's data indicate that 50 percent of people who begin the online process of booking a flight never complete the process and pay for the flight. To reduce this percentage, the airline is considering changing its website so that the entire booking process, including flight and seat selection and payment, can be done on two simple pages rather than the current four pages. A random sample of 300 customers who begin the booking process are exposed to the new system, and 117 of them do not complete the process. a. Formulate the null and alternative hypotheses needed to attempt to provide evidence that the new system has reduced the noncompletion percentage. b. Use critical values to perform the hypothesis test by setting α equal to .10, .05, .01, and .001

When a famous painting becomes available for sale, it is often known which museum or collector will be the likely winner. Yet, the auctioneer actively woos representatives of other museums that have no chance of winning to attend anyway. Suppose a piece of art has recently become available for sale and will be auctioned off to the highest bidder, with the winner paying an amount equal to the second highest bid. Assume that most collectors know that Valerie places a value of $15,000 on the art piece and that she values this art piece more than any other collector. Suppose that if no one else shows up, Valerie simply bids $15,000/2=$7,500 and wins the piece of art. The expected price paid by Valerie, with no other bidders present, is $________.. Suppose the owner of the artwork manages to recruit another bidder, Antonio, to the auction. Antonio is known to value the art piece at $12,000. The expected price paid by Valerie, given the presence of the second bidder Antonio, is $_______. .

From the given graph solve all three true or false statements.

According to a recent Wall Street Journal article, about 2% of new US car sales are electric vehicles (data from Edison Electric Institute reported by Jinjoo Lee, "Peak Oil? Not This Year. Or This Decade," January 9, 2021 pg. B12). Suppose a company has 111 employees who drive new cars (separately) to work each day. What is the probability that at least one of them will drive an electric car? Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.

A lottery has a grand prize of $1,000,000, 2 runner-up prizes of $100,000 each, 6 third-place prizes of $10,000 each, and 19 consolation prizes of $1,000 each. If a 4 million tickets are sold for $1 each, and the probability of any ticket winning is the same as that of any other winning, find the expected return on a $1 ticket. (Round your answer to 2 decimal places.

Let X1, X2, X3, X4 have the joint probability density functionf(x1, x2, x3, x4) = (24e−(x1+x2+x3+x4), 0 < x1, x2, x3, x4 < ∞0, elsewhereLet Y1 = X1, Y2 = X2 − X1, Y3 = X3 − X2, Y4 = X4 − X3.(i) Using the change of variable technique, find the joint probability density functionof Y1, Y2, Y3, Y4(ii) Find the conditional distribution of Y4 given Y1, Y2, Y3

The promoter of a football game is concerned that it will rain. She has the option of spending ​$14,040 on insurance that will pay ​$39,000 if it rains. She estimates that the revenue from the game will be ​$65,040 if it does not rain and ​$30,040 if it does rain. What must the chance of rain be if buying the policy has the same expected return as not buying​ it? Write expressions showing the expected returns if the promoter does and does not purchase the​ insurance, using p to represent the probability of rain.   Without​ insurance, E(return)​ =   With​ insurance, E(return)​ =   The chance of rain must be _%.

How Gauss–Markov Theorem is applied when X Is Nonrandom?

Arielle is a risk-averse traveler who is planning a trip to Canada. She is planning on carrying $400 in her backpack. Walking the streets of Canada, however, can be dangerous and there is some chance that she will have her backpack stolen. If she is only carrying cash and her backpack is stolen, she will have no money ($0). The probability that her backpack is stolen is 1/5. Finally assume that her preferences over money can be represented by the utility function U(x)=(x)^0.5 Suppose that she has the option to buy traveler’s checks. If her backpack is stolen and she is carrying traveler’s checks then she can have those checks replaced at no cost. National Express charges a fee of $p per $1 traveler’s check. In other words, the price of a $1 traveler’s check is $(1+p).             If the purchase of traveler’s checks is a fair bet, then we know that the purchase of traveler checks will not change her expected income. Show that if the purchase is a fair bet, then the price (1+p) = $1.25.

Find the values of Absolute Risk Aversion (ARA) and Relative Risk Aversion (RRA) for all the cases below. .         U(C) = C0.5. .         U(C) = C2. .         U(C) = 5×C. .         U(C) = -C-2. .         U(C) = -C-7. .         U(C) = -e-7C. .         U(C) = [1/(1-a)]×C1-a , where a is a constant.

Suppose that Var(X) = 661.1, Var(X) = 8021.53, and Cov(X,Y) = 1922.11. What is Var(.64X + .36Y)?   Suppose that Var(X) = 869.03, Var(X) = 7850.84, and Cov(X,Y) = 2238.69. What is Var(.67X + .33Y)?

Max Pentridge is thinking of starting a pinball palace near a large Melbourne university. His utility is given by u(W) = 1 - (5,000/W), where W is his wealth. Max's total wealth is $15,000. With probability p = 0.9 the palace will succeed and Max's wealth will grow from $15,000 to $x. With probability 1 - p the palace will be a failure and he’ll lose $10,000, so that his wealth will be just $5,000.  What is the smallest value of x that would be sufficient to make Max want to invest in the pinball palace rather than have a wealth of $15,000 with certainty? (Please round your final answer to the whole dollar, if necessary)

Gary likes to gamble. Donna offers to bet him $31 on the outcome of a boat race. If Gary’s boat wins, Donna would give him $31. If Gary’s boat does not win, Gary would give her $31. Gary’s utility function is p1x^21+p2x^22, where p1 and p2 are the probabilities of events 1 and 2 and where x1 and x2 are his wealth if events 1 and 2 occur respectively. Gary’s total wealth is currently only $80 and he believes that the probability that he will win the race is 0.3. Which of the following is correct? (please submit the number corresponding to the correct answer). Taking the bet would reduce his expected utility. Taking the bet would leave his expected utility unchanged. Taking the bet would increase his expected utility. There is not enough information to determine whether taking the bet would increase or decrease his expected utility. The information given in the problem is self-contradictory.

Suppose that Winnie the Pooh and Eeyore have the same value function: v(x) = x1/2 for gains and v(x) = -2(|x|)1/2 for losses. The two are also facing the same choice, between (S) $1 for sure and (G) a gamble with a 25% chance of winning $4 and a 75% chance of winning nothing. Winnie the Pooh and Eeyore both subjectively weight probabilities correctly. Winnie the Pooh codes all outcomes as gains; that is, he takes as his reference point winning nothing. For Pooh: What is the value of S? What is the value of G? Which would he choose? Eeyore codes all outcomes as losses; that is, he takes as his reference point winning $4. For Eeyore: What is the value of S? What is the value of G? Which would he choose?