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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).
An approximation to the error of a Riemannian sum: where V g (a; b) is the total variation of g on [a, b] de ned by the sup over all partitions on [a, b], including (a; b
Consider the following game: (a) If (top, left) is a Weakly Dominant Strategy Equilibrium, then what inequalities must hold among (a, ..., h)? (b) If (top, left) is a Na
Coefficient of Variation The standard deviation discussed above is an absolute measure of dispersion. The corresponding relative measure is known as the coefficient of vari
Investigate the use of fixed and percentile meshes when applying chi squared goodness-of- t hypothesis tests. Apply the oversmoothing procedure to the LRL data. Compare the res
Correlation The correlation is commonly used and a useful statistic used to describe the degree of the relationships between two or more variables. Pearson's correlation refle
"MagTek" electronics has developed a smart phone that does things that no other phone yetreleased into the market-place will do. The marketing department is planning to demonstrate
the sum of mean and variance ofabinomia distribution of 5 trials is 9/5, find the binomial distribution.
Empirical Mode Where mode is ill-defined, its value may be ascertained by the following formula based upon the empirical relationship between Mean, Median and Mode: Mode = 3
Prediction Inte rval We would like to construct a prediction interval around which would contain the actual Y. If n ≥ 30, ± Zs e would be the interval, where Z
Calculation for Continuous Series or Grouped Data = where, m = mid-point of class =
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