Consider the joint PMF given by x + y f(x,y) = ,X = 1,2,y= 1,2,3,4 32 a) Find g(x), the marginal distribution of X (b) Find f(x\y), the conditional distribution of X given Y=y c) Calculate P(X< Y) d) Calculate P(X = 1 | Y = 2)
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- An individual has the utility function U(I) = I^(1/2), where I is their net income. (Note that I to the exponent/power of 1/2 is the same as the square root of I.) The individual starts with $1600 in income. The individual has a 20% probability of being very sick, 30% probability of being slightly sick, and 50% probability of being healthy. If the individual is sick, they lose net income because they need to pay healthcare costs. The healthcare costs are $1600 if they are very sick, $700 if they are slightly sick, and $0 if they are healthy. Please use this information for the following parts of this question unless otherwise specified. What is the individual's expected utility? Suppose a health insurance company offers the individual a full insurance contract. What is the actuarially fair, full insurance premium for this individual? What is the individual's expected utility if they purchase a full insurance contract at the actuarially fair, full insurance premium?Please do not give solution in image format thanku Two Manufacturers supply food to a large cafeteria. Manufacturer A supplies 40% of the soup served in the cafeteria, while Manufacturer B supplies 60% of the soup that is served. 3% of the soup cans provided by Manufacturer A are found to be dented, while 1% of the cans provided by Manufacturer B are found to be dented. Given that a can of soup is dented, find the probability that it came from Manufacturer B.A software developer makes 175 phone calls to its current customers. There is an 8 percent chance of reaching a given customer (instead of a busy signal, no answer, or answering machine). The normal approximation of the probability of reaching at least 20 customers is Multiple Choice .022 .007 .063 .937
- Show that a decision maker who has a linear utilityfunction will rank two lotteries according to their expectedvalue.John wants to buy a used car. He knows that there are two types of car in the market, plums and lemons. Lemons are worse quality cars and are more likely to break down than plums. John is willing to pay £10, 000 for a plum and £2, 000 for a lemon. Unfortunately, however, he cannot distinguish between the two types. Sellers can offer a warranty that would cover the full cost of any repair needed by the car for y ∗ years. Considering the type and likelihood of problems their cars can have, owners of plums estimate that y years of guarantee would cost them 1000y, owners of lemons estimate that the cost would be 2000y. John knows these estimates and decides to offer £10, 000 if a car comes with y ∗ years of warranty, £2, 000 if a car comes without warranty. For which values of y ∗ is there a separating equilibrium where only owners of plums are willing to offer the y ∗ -years warranty? Clearly explain your reasoning.JUST ANSWER SUBPART 2 There are two individuals, Individual A and Individual B. Individual A has an income (Y) of 500 million Rupiah per year. If Individual A is sick, he will lose 25% of his income. Meanwhile, Individual B has an income (Y) of 100 million Rupiah per year, and if Individual B is sick, he will lose 75% of his income. The probability of Individual A and Individual B being sick is the same, which is 10%. If the satisfaction level of Individual A and Individual B is determined by their income level, based on the following function U(Y)=ln Y, would Individual A and Individual B prefer not to have health insurance? Explain Faced with fair actuarially insurance, how much premium is offered to Individual A? Is the premium rate offered the same for Individual B? Explain with the support of graphic illustrations. The government decides to provide compulsory health insurance with a premium rate for Individual A and Individual B, which is 2% of the income of each individual. In…
- The application which provides a way of revising conditional probabilities by using available information and provisions for revising conditional probabilities with other information that is useful for management decision making is called? Select one: a. Bayes’ theorem. b. overinvolvement ratios. c. probability rules. d. empirical formula.Two identically able agents are competing for a promotion. The promotion is awarded on the basis of output (whomever has the highest output, gets the promotion). Because there are only two workers competing for one prize, the losing prize=0 and the winning prize =P. The output for each agent is equal to his or her effort level times a productivity parameter (d). (i.e. Q2=dE1 , Q2=dE2). If the distribution of “relative luck” is uniform, the probability of winning the promotion for agent 1 will be a function of his effort (E1) and the effort level of Agent 2 (E2). The formula is given by...Prob(win)=0.5 + α(E1-E2), where α is a parameter that reflects uncertainty and errors in measurement. High measurement errors are associated with small values of α (think about this: if there are high measurement errors, then the level of an agent’s effort will have a smaller effect on his/her chances of winning). Using this information, please answer the following questions. Both workers have a…You are taking a multiple-choice test that awards you one point for a correct answer and penalizes you 0.25 points for an incorrect answer. If you have to make a random guess and there are five possible answers, what is the expected value of guessing? Group of answer choices -0.25. 0.25. 0.5. 1. 0.
- If a person lives for 3 years with a disease and the current standard of care for that disease means he/she lives with a utility level of 0.7.-What is the QALY? Answer in not less than 300 wordsYou hold an oral, or English, auction among three bidders. You estimate that each bidder has a value of either $40 or $50 for the item, and you attach probabilities to each value of 50%. The winning bidder must pay a price equal to the second highest bid. The following table lists the eight possible combinations for bidder values. Each combination is equally likely to occur. On the following table, indicate the price paid by the winning bidder. Combination Number Bidder 1 Value Bidder 2 Value Bidder 3 Value Probability Price ($) ($) ($) 1 $40 $40 $40 0.125 2 $40 $40 $50 0.125 3 $40 $50 $40 0.125 4 $40 $50 $50 0.125 5 $50 $40 $40 0.125 6 $50 $40 $50 0.125 7 $50 $50 $40 0.125 8 $50 $50 $50 0.125 The expected price paid is . Suppose that bidders 1 and 2 collude and would be willing to bid up to a maximum of their values, but the two bidders would not be willing to bid against each…Suppose that there are two types of workers: high and low. Employers cannot distinguish between different types during an interview. Employers value high type at $200,000 and low type at $100,000. Employers are in a competitive market (i.e. zero profit applies). High type workers have a reservation wage of 140,000 and low type workers have a reservation wage of 80,000. Suppose that 50% of all workers are high type. The productivities, reservation wages, and the probabilities are common knowledge). What wage would the employers offer? Please explain the solution!
