Assume that you maximize expected utility with linear utility function u(x) = x. Let P denote your subjective probabilities. In particular, assume that you assign to the event E the subjective probability P (E). Consider the quadratic scoring rule, which is used to elicit subjective probabilities in experiments. Under the quadratic scoring rule you have to choose a number r between 0 and 1, called your reported probability of E, and receive the act (E : 1 −(1 −r)2; EC: 1 −r2). Which number do you choose (to be expressed in terms of P (E))?

Assume that you maximize expected utility with linear utility function u(x) = x. Let P denote your subjective probabilities. In particular, assume that you assign to the event E the subjective probability P (E). Consider the quadratic scoring rule, which is used to elicit subjective probabilities in experiments. Under the quadratic scoring rule you have to choose a number r between 0 and 1, called your reported probability of E, and receive the act (E : 1 −(1 −r)2; EC: 1 −r2). Which number do you choose (to be expressed in terms of P (E))?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

Ma1.

Assume that you maximize expected utility with linear utility function u(x) = x. Let P

denote your subjective probabilities. In particular, assume that you assign to the event

E the subjective probability P (E). Consider the quadratic scoring rule, which is used to

elicit subjective probabilities in experiments. Under the quadratic scoring rule you have to

choose a number r between 0 and 1, called your reported probability of E, and receive the

act (E : 1 −(1 −r)2; EC: 1 −r2). Which number do you choose (to be expressed in terms

of P (E))?

Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.

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