You have drawn a painting that you want to sell to an anonymous buyer, but you do not know exactly how much they are willing to pay. Based on past experiences, you estimate that the buyer will be willing to pay in monetary units where a random variable is evenly distributed continuously over the interval [200, 500]. Let's assume that your assessment regarding the random variable is correct, i.e., that it is indeed evenly distributed continuously over the interval [200, 500]. What price �p will you choose if you want to maximize your expected profit? What will be your expected profit?

To examine the effectiveness of its four annual advertising promotions, a mail order company has sent a questionnaire to each of its customers, asking how many of the previous year's promotions prompted orders that would not have otherwise been made. The accompanying table lists the probabilities that were derived from the questionnaire, where X is the random variable representing the number of promotions that prompted orders. If we assume that overall customer behavior next year will be the same as last year, what is the expected number of promotions that each customer will take advantage of next year by ordering goods that otherwise would not be purchased? Expected value = A previous analysis of historical records found that the mean value of orders for promotional goods is 31 dollars, with the company earning a gross profit of 23% on each order. Calculate the expected value of the profit contribution next year. Expected value = хо 1 2 3 4 P(X) 0.1 0.203 0.313 0.177 0.207 The fixed…

The Census Bureau includes nine states in what it defines as the Northeast region of the United States. Assume that the government is interested in tracking unemployment in these nine states and that the random variable of interest is the number of Northeastern states with an unemployment rate that is less than 8.3%. What values may this random variable assume? (Enter your answers as a comma-separated list.)

A proprietor of a food-stall has invented a new item of food delicacy which he calls WHIM. He has calculated that the cost of manufacture is Re. 1 per piece and that because of its novelty and quality it would be sold for Rs. 3 per piece. It is, however, perishable, and any goods unsold at the end of the day are a dead loss. He expects the demand to be variable and has drawn up the following probability distribution. 14 No. of pieces demanded : Probability (i) Find the value of k. 10 11 12 13 15 k + 0:02 k + 0.05 5k -0.02 7k + 0:03 2k + 0-02 2k (ii) Find an expression for his net profit or loss if he manufactures m pieces and only n are demanded; consider separately the two cases n m. (ii) Assume that he manufactures 12 pieces. using the result in (i) ab ove, find his net profit or loss for ea ch level of demand. (v) Also obtain the net profits for di fferent levels of demand and produ ction, each ranging from 10 to 15. (iv) Using the probability distributio n, calculate his expected…