1. The probabilities associated with the expected principal source of payment for the hospitai discharges in the United States in the year 1990 are listed below. Principal source of payment | Probability Private insurance Medicare Medicaid Other Govt. Program Self-payment Other/no charge 0.387 0.345 0.116 0.033 0.058 0.028 Not stated 0.033 Total 1.00 What is the probability that the principal source of payment for a given hospital discharge a. is the patient's private insurance. OY b. What is the probability that the principal source of payment is Medicare, Medicaid, or some other government program? с. Given that the principal source of payment is a Government program what is the probability that it is a Medicare.

2. Statistical measures of stand-alone risk Remember, the expected value of a probability distribution is a statistical measure of the average (mean) value expected to occur during a possible circumstances. To compute an asset's expected return under a range of possible circumstances (or states of nature), multiply the anticipated return expected to result during each state of nature by its probability of occurrence. Consider the following case: Ethan owns a two-stock portfolio that invests in Happy Dog Soap Company (HDS) and Black Sheep Broadcasting (BSB). Three- quarters of Ethan's portfolio value consists of HDS's shares, and the balance consists of BSB's shares. Each stock's expected return for the next year will depend on forecasted market conditions. The expected returns from the stocks in different market conditions are detailed in the following table: Market Condition Probability of Occurrence Happy Dog Soap Black Sheep Broadcasting Strong 0.50 50% 70% Normal 0.25 30% 40% Weak…

1/ A company is going to release four quarterly reports this year. Suppose the company has a 35% chance of beating analyst expectations each quarter. a. What is the probability that the company beats analyst expectations every quarter of this year? b. What is the probability the company beats analyst expectations more than half the time this year? c. What is the expected number of times the company will beat analyst expectations this year?

For 10 percent of the products in a category, a firm fails to satisfy all demand during themonth. What is its in-stock probability?

What is the difference between discrete and continuous probability distributions? What are six situations in which a variable of interest may be considered either continuous or discrete?

Suppose best buy offers an extended warranty for $25 on an electronic device whose value is $250. Suppose best buy estimates the probability the item will be returned for a claim on that warranty is 5%. Assume that if an item is returned, best buy will refund the $250 purchase price. What is best buys expected value on the warranty?

Suppose a life insurance company sells a ​$230,000 ​one-year term life insurance policy to a 20​-year-old female for ​$370.The probability that the female survives the year is 0.999464. Compute and interpret the expected value of this policy to the insurance company.

Suppose a life insurance company sells a ​$230,000 ​one-year term life insurance policy to a 20​-year-old female for​$240. The probability that the female survives the year is 0.999463. Compute and interpret the expected value of this policy to the insurance company.

An insurance policy on an electrical device pays a benefit of $2400 if the device fails during the first year. The amount of the benefit decreases by $800 each successive year until it reaches 0 . If the device has not failed by the beginning of any given year, the probability of failure during that year is 0.29.Find the expected benefit under this policy.

Suppose a life insurance company sells a $280,000 one-year term life insurance policy to a 24​-year-old female for $180. The probability that the female survives the year is 0.999522. Compute and interpret the expected value of this policy to the insurance company.