What are the states of nature

Reference no: EM13965275

Problem 1: A coin (not necessarily fair) will be tossed once, and you have to predict the outcome. If you predict the outcome correctly you win $1000. Otherwise, you lose $5.

(a) What are the states of nature? What is the decision space? Write the utility table.

(b) Suppose that you believe that the probability of heads is 2/3. What is your price for the states of nature? Find the expected gains.

(c) Suppose that you are allowed to toss the coin twice and you ?nd that the ?rst toss results in heads and the second in tails. What are the observables?

(d) Assume the situation in (c). The coin is going to be tossed again and you have to predict the outcome. What is your updated prior?

(e) What are your expected gains, and what is your decision for the situation in (d)?

Reference no: EM13965275

Questions Cloud

Find angles of incidence and refraction at each interface : A converging lens of focal length 10 cm is placed 35 cm in front of a concave mirror with a radius of curvature of 20 cm. An object is placed 13 cm in front of the lens. Locate and describe the final image, and determine its net magni?cation. (ray..

Lower-level managerial personnel : The following data represent a random sample of end-of-year bonuses for the lower-level managerial personnel employed by a large ?rm. Bonuses are expressed in percentage of yearly salary.

What is the bayes decision : That is, P (X = x1|θ1) = 0.1 or P (X = x2|θ3) = 0.4, and so forth. Suppose you observe X1; what is the updated prior? What is the Bayes decision?

Uniform prior for the states of nature : Determine the Bayes decision assuming a uniform prior for the states of nature.

What are the states of nature : (a) What are the states of nature? What is the decision space? Write the utility table. (b) Suppose that you believe that the probability of heads is 2/3. What is your price for the states of nature? Find the expected gains.

Chance of economic expansion or status : Suppose a government forecast indicates that there is a 70% chance of economic expansion or status quo in the next 4 years and there is a 30% chance that the economy will show a decline. What is the optimal decision in this problem? Did you make a..

?ips of a balanced coin : Suppose that we will receive $25 if we get two consecutive heads (H) on two ?ips of a balanced coin. If only one head appears, we will get $10. On the other hand, if there is no heads, we will lose $15. If monetary return is the only concern, shou..

Estimating probability of heads : Suppose we have a coin (not necessarily balanced) with p being the probability of heads. Assume a uniform prior for p. Suppose in 20 tosses of this coin, we obtained 12 heads. Test the hypothesis H0 : p ≥ 0.50 vs. Ha : p > 0.50.

What is the image distance : Convex mirrors are being used to monitor the aisles in a store. The mirrors have a radius of curvature of 4 m. What is the image distance if a customer is 19 m in front of the mirror?

User Account

All Pages