Suppose that, in a particular city, airport A handles 50% of all airline traffic, and airports B and C handle 30% and 20%, respectively. The detection rates for weapons at the three airports are .9, .5, and .4, respectively. If a passenger at one of the airports is found to be carrying a weapon through the boarding gate, what is
Jamba juice is considering selling juices along with its other products. States of Nature High Sales Med. Sales Low Sales A(0.2) B(0.5) C(0.3) A1 (sell juices) 3000 2000 -6000 A2 (don't sell juices) 0 0 0 The probabilities shown above represent the states of nature and the decision maker's (e.g., mana
A Committee of three people has been formed by random selection from five left-wingers and four right wingers. The Committee members then vote for or against a strike whenever there is a dispute. Each left winger votes for a strike three out of four times in strike votes, whereas each right winger votes for a strike only once ou
Assume that a patient is believed to have one of two diseases, denoted by D1 and D2 with P(D1)=0.40 and P(D2)=0.60 and that medical research has determined the probability associated with each symptom that may accompany the diseases. Suppose that given diseases D1 and D2, the probabilities that the patient will have symptom S1,
a. See the attached file for the chart of data pertaining to this question. The probabilities shown above represent the states of nature and the decision maker's (e.g., manager) degree of uncertainties and personal judgment on the occurrence of each state. What is the expected payoff for actions A1 and A2 above? What would b
The original questions were: a. CoffeeTime is considering selling juices along with its other products. States of Nature High Sales Med. Sales Low Sales A(0.2) B(0.5) C(0.3) A1 (sell juices) 3000 2000 -6000 A2 (don't sell juices) 0 0 0 The probabilities shown above represent the s
(See attached file for full problem description) --- CoffeeTime is considering selling juices along with its other products. States of Nature High Sales Med. Sales Low Sales A(0.2) B(0.5) C(0.3) A1 (sell juices) 3000 2000 -6000 A2 (don't sell juices) 0 0 0 The probabilities shown above represent the
Suppose theta is a parameter that takes values on the real line. Consider the loss function l(theta, theta_hat) = 0 if |q-theta_hat|<=c, 1 otherwise Show that the Bayes estimate of theta is the midpoint of the interval I of length 2c that maximizes P(theta in I|x).
Suppose that the loss function is l(theta, theta_hat) = |theta - theta_hat|. Show that the Bayes estimate of theta is any median of the posterior distribution (any number m(x) such that P(theta <= m(x)|x)>=.5 and P(theta>=m(x)|x)>=.5).
Over the 48 years from 1950 through 1997, the stock market has gone up in the month of January for 31 times; it has gone up for the whole year for 36 times, and it has gone up both for the year and in January for 29 times. 1) Based on historical data, what is the probability the stock market will go up in January? 2) B
Question: Urn I has 2 white and 3 black balls; Urn II, 4 white and 1 black; and Urn III, 3 white and 4 black. An urn is selected at random and a ball drawn at random is found to be white. Find the probability that Urn I was selected. Answer: 14/57
Category: Statistics Subject: probabilities and Bayes theorem Details: 1. (Independence of events). The chancellor of a state university is applying for a new position. At a certain point in his application process, he is being considered by seven universities. At three of the seven he is a finalist, which means that he
How do I derive the posterior density of a Weibull Distribution?
Experience has shown a company that the cost of delivering a small package within 24 hours is $14.80. The company charges $15.50 for shipment but guarantees to refund the charge if delivery is not made within 24 hours. If the company fails to deliver only 2% of its packages within the 24-hour period, what is the expected gain