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An approximation to the error of a Riemannian sum:
where Vg(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) = (-∞, ∞). Con- clude that if f'(.)2 has nite total variation, then the remainder term in the bias (3.14) is O(h3).
Compute the roughness of several parametric densities: Cauchy, Student's t, Beta, lognormal. For each compute the optimal bin width. Express the optimal bin width in terms of the variance, if it exists.
PROPERTIES 1. The value of standard deviation remains the same if, in a series each of the observation is increased or decreased by a constant quantity. In statistical lan
Replacement times for TV sets are normally distributed with a mean of 8.2 years and a standard deviation of 1.1 years. Find the replacement time that separates the top 20% from the
Index Number Meaning and Definitions of Index Number The index numbers are the special type of averages which are presented in percentages and computed on certain base.
Suppose that in the actual survey of 50 prospective customers, 6 subscribe to the 3 for all offer, what does this tell you about the previous estimate of the proportion of customer
Suppose that before the minimum wage law change, the underlying mean number of part-time employees per Burger King Restaurant in New Jersey was 20.3. It was thought that the increa
Find unlabeled data set test.txt and initial centroids data set centroids.txt in the archive, both files have the following format: [attribute1_value attribute2_value ...
(a) At a stream gauging station, the following discharges and stage measurements were taken for the purpose of the rating curve at that section: Stage (m) 1
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
When the number of farmers growing wheat in Russia increases, the increase in world supply lowers the world price of wheat. Draw an appropriate diagram to analyze how this chang
The calculations of arithmetic mean may be simple and foolproof, but the application of the result may not be so foolproof. An arithmetic mean may not merely lack
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