An insurance company charges a customer an annual premium of $1200 to I insure a car against theft. In the event of theft a payment of $15 000 will be made to the customer. The probability of theft is empirically estimated to be 0.02. (a) (b) Find the expected value of the insurance policy to the customer. Find the premium which should be charged if the policy is to be fair.
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- Please no written by hand solution Kate recently invested in real estate with the intention of selling the property one year from today. She has modeled the returns on that investment based on three economic scenarios. She believes that if the economy stays healthy, then her investment will generate a 30 percent return. However, if the economy softens, as predicted, the return will be 10 percent, while the return will be -25 percent if the economy slips into a recession. If the probabilities of the healthy, soft, and recessionary states are 0.6, 0.2, and 0.2, respectively, then what are the expected return and the standard deviation of the return on Kate❝s investment? Calculate the coefficient of variation for this investment. (Round expected return to 3 decimal places, e.g. 0.125 and round intermediate calculations and standard deviation to 5 decimal places, e.g. 0.07680.)1. Imagine a person who wants to find a job within two months. Define X corresponding to the outcome, such that X = 1 if the person finds a job and X = 0 otherwise. (a) Explain why X can be viewed as a random variable. What is the support of X? (b) Suppose the probability of finding a job is 0.75. What is the probability distribution of X? Be specific.The probabilities of X, Y and Z becoming managers are 4/9, 2/9 and 1/3 respectively. The probabilities that the Bonus Scheme will be introduced if X, Y and Z becomes managers are 3/10, 1/2, and 4/5 respectively. (i) What is the probability that Bonus Scheme will be introduced, and (ii) if the Bonus Scheme has been introduced, what is the probability that the manager appointed was X ?
- 6 Company “X Star" supplies electronic devices. Probability of purchasing a defective device is 0.3. Mr. Chang has purchased two devices. (a) What is the probability that at least one device purchased by Mr. Chang is good? (b) What is the probability that at least one device purchased by Mr. Chang is defective?The owner of Tastee Cookies needs to decide whether to lease a small, medium, or large new retail outlet. She estimates that monthly profits will vary with demand for her cookies as follows: SIZE OFOUTLET DEMAND LOW HIGH Small $ 1,000 1,000 Medium 500 2,500 Large 0 3,000 For what range of probability that demand will be high, will she decide to lease the medium facility?21 Los Angeles averages 266.5 sunny days per year. What is probability that Boston has at least as many sunny days as Los Angeles? a 0.0020 b 0.0031 c 0.0047 d 0.0073
- The frequency of breakdown of a machine per month is shown in the table. The cost ofa breakdown is $1,000 and the cost of preventive maintenance is $1,250 per month. Ifpreventive maintenance is performed, the probability of a machine breakdown is negligible. Should the manager use preventive maintenance, or would it be cheaper to repair themachine when it breaks down?Number of breakdowns 0 1 2 3Frequency of occurrence .20 .30 .40 .10Q. 2. Explain why there must be mistake in the following statement: "A quality control engineer claims that the probability that a large consignmen of glass bricks contians 0, 1, 2, 3, 4 or 5 defectives are 0-11%; 0-23, 0-37, 0-26, 0-009 and 0-05 respectively".A market research firm is interested in surveying certain attitudes in a small community. There are 125 households broken down according to income, ownership of a telephone or ownership of a T.V. Household with monthly Household with monthly 8.000 income of " 8,000 or less Telephone Subscriber income above No Telephone Telephone SubsNcriber No. Telephone Own 7V. set 27 20 18 10 No. T.V. set 18 10 12 10 (i) What is the probability of obtaining of a TV. owner in drawing at random ? (ii) If a household has monthly income over Rs. 8,000 and is a telephone subscriber, what is the probability that it has a T.V. ? (iii) What is the conditional probability of drawing a household that owns a T.V., given that the household is a telephone subscriber ? (iv) Are the events 'ownership of a T.V.' and 'telephone subscriber statistically independent ? Comment.
- Probability Possible Rate of Return 0.25 -0.10 0.15 0.00 0.35 0.10 0.25 0.25 a. Under what conditions can the standard deviation be used to measure the relative risk of two investments? b. Under what conditions must the coefficient of variation (CoVar) be used to measure the relative risk of two investments?1 A car dealer has established that 40% of his potential customers prefer single cab cars while 60% prefer double cab cars. From a recent survey among his existing clients, he obtained additional information which indicates that 15% of clients who bought single cab cars prefer air conditioning while 65% of clients who bought double cars prefer air conditioning.Required:a) What is the probability that a client who bought a single cab does not prefer air conditioning? (5)b) What is the probability that a client prefers a double cab with air conditioning?cam A-e47239db-071d-490b-8d5... Q Search c) If a computer monitor is found to be defective, to two decimal places, what is the probability it came from supplier B ? 20. Decision Analysis: An oil company is considering drilling at two different sites. However, it can only afford to commit its resources to one site. It is estimated that site A will net $35 million if successful (probability .25) and lose $3 million if not successful. Site B will net $48 million if successful (probability .2) and lose $4 million if not successful. What is the expected return from each site? Which site should the oil company choose? I