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- If a game gives payoffs of $10 and $100 with probabilities 0.9 and 0.1, respectively, then the expected value of this game is E=0.9+0.1= .A forest consists of two types of trees; young (between 0 and 3 m tall) and adults (more than 3 m). Each year, 20% of young trees die, 10% sell for $20 each, 30% remain between 0 and 3 m, and 40% grow taller than 3 m. Each year, 40% of adult trees sell for $50, 20% sell for $20, 30% remain in the forest, and 10% die. If it costs $5 to plant a tree, what is the expected profit for each tree planted?Suppose a company charges an annual premium of $110 for an insurance policy for minor injuries. Actuarial studies show that in case of an injury claim, the company will pay out an average of $900 for outpatient care and an average of $3000 for an overnight stay in the hospital. They also determine that, on average, each year there are five claims made that result in outpatient care for every 1000 policies and three claims made that result in an overnight stay out of every 1000 policies. What is the expected annual profit of an insurance policy for the company?
- A company estimates that 0.1% of their product will fail after th original warranty period but within 2 years of the purchase, with a replacement cost of $350. If they offer a 2 year warranty for $18 , what is the company's expected value of each warranty sold?Suppose that during a recent 30-year period, there were eight volcanic eruptions sufficiently powerful to reduce the amount of power generated by solar panels by at least 20% for a period of a year. Call these "Class D20" volcanoes. Suppose that the return on investment from installing solar panels is often calculated over a 25-yearperiod. What is the probability that, during a 25-year period, there will be two or more "Class D20" volcanic eruptions?A forward contract exists for a unit of two-year government securities with delivery to take place three years from now. Suppose the price of these securities three years from now is uniformly distributed from a low $800 to a high of $1,400. The one-year expected riskless rate of interest is 5 percent for all periods under consideration. If investors are risk neutral, what should be the current forward price? Suppose now that investors are risk averse and that the forward price is $1,200. What do you know about the relationship between the market value of two-year government securities and overall consumption? Continue to assume (as in (ii)) that the current forward price (at time 0) is $1,200. One year from now (at time 1) the forward price for the same item and same delivery date is $1,000. Determine the time 1 value (to the buyer) of the contract that was agreed upon at time 0.
- Suppose that a life insurance company insures 900,000 fifty-year-old people in a given year. (Assume a death rate of 8 per 1000 people.) The cost of the premium is $500 per year, and the death benefit is $45,000. What is the expected profit or loss for the insurance company?A company makes electronic gadgets. One out of every 20 gadgets is faulty, but the company doesn’t know which ones are faulty until a buyer complains. Suppose the company makes a $8 profit on the sale of any working gadget, but suffers a loss of for every faulty gadget because they have to repair the unit. What is the expected profit or loss for every batch of 20 gadgets sold?Suppose that a life insurance company insures 1 million 50-year-old people in a given year. (Assume a death rate of 5 per 1000 people.) The cost of the premium is $200 per year, and the death benefit is $50,000 What is the expected profit or loss for the insurance company?
- Consider two people age 40. What is the expected number of years that both are alive? What is the expected number of years that at least one is alive? Show your work in excel to solve the following: What is the actuarial present value of a pension that pays $50,000 per year as long as at least one of the two 40-year-old people survive? Use a 5% discount rate. [Remember actuarial present value means that you must discount in the usual way to get present value, but you also must weight (i.e., multiply) every yearly payment by the probability that at least one of the two 40-year-old people is alive in order to receive the $50,000 payment.]A contractor has to choose between two jobs. The first promises a profit of Rs. 1,20,000 with a probability of 3⁄4 or a loss of Rs. 30,000 due to delays with a probability of 1⁄4; the second promises a profit of Rs. 1,80,000 with a probability of 1⁄2 or loss of Rs. 45,000 with a probability of 1⁄2 . Which job should the contractor choose so as to maximize his expected profit?The United States Department of Agriculture (USDA) found that the proportion of young adults ages 20–39 who regularly skip eating breakfast is 0.2380.238. Suppose that Lance, a nutritionist, surveys the dietary habits of a random sample of size ?=500n=500 of young adults ages 20–39 in the United States. Apply the central limit theorem to find the probability that the number of individuals, ?,X, in Lance's sample who regularly skip breakfast is greater than 126126. You may find table of critical values helpful. Express the result as a decimal precise to three places. Then, Apply the central limit theorem for the binomial distribution to find the probability that the number of individuals in Lance's sample who regularly skip breakfast is less than 9898. Express the result as a decimal precise to three places.