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If the economy does well, the investor's wealth is 2 and if the economy does poorly the investor's wealth is 1. Both outcomes are equally likely. The investor is offered to invest in shares of a project that gains 3=2 if the economy does well and loses 1 if the economy does poorly. Therefore, if the investor obtains α shares of this project his wealth is 2 + 3α/2
with probability 1/2 and 1= α with probability 1/2. The investor is an expected utility maximizer with utility index u(z) = ln z. What is the optimal α for this investor? ( α must be between 0 and 1).
Variance The term variance was used to describe the square of the standard deviation by R.A.Fisher. The concept of variance is highly important in areas where it is possible to
Lifts usually have signs indicating their maximum capacity. Consider a sign in a lift that reads "maximum capacity 1400kg or 20 persons". Suppose that the weights of lift-users are
Mode The mode is the value which occurs most frequently in a set of observations on the point of maximum frequency and around which other items of the set cluste
For many decades, there has been considerable attention paid to identifying various factors that help to reduce the number of fatalities on Australian roads. In 1964 Victoria and S
The Harmonic Mean is based on the reciprocals of numbers averaged. It is defined as the reciprocal of the arithmetic mean of the reciprocal of the given individual observations. Th
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(1) Assume we categorize voters in a city as havingless educationand those havingmoreeducation. Those with less education have less than a college degree; those with more education
Harmonic Mean The harmonic mean also called harmonic average, in the total numbers of items of variable divided by the sum of r reciprocals of the values of the variable. In
What is an interaction? Describe an example and identify the variables within your population (work, social, academic, etc.) for which you might expect interactions?
Calculation of Degrees of Freedom First we look at how to calculate the number of DOF for the numerator. In the numerator since we calculate the variance from the sample means,
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