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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.
For the circuit shown below; Write a KCL equation for Node A, Node B, Node C and Node D. Write a KVL equation for Loop 1, Loop 2 and Loop 3. A simple circ
The investor has constant wealth 1 and is o?ered to invest in shares of a project that either gains 3=2 or loses 1 with equal probabilities. Therefore, if the investor obtains sha
Multivariate analysis involves a set of techniques to analyse data sets on more than one variable. Many of these techniques are modern and often involve quite sophisticated use of
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
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 ...
The weight of the engine in kN is given in P2 and is suspended from a vertical chain at A. A second chain round the engine is attached at A, with a spreader bar between B and C. Th
a) What is meant by secular trend? Discuss any two methods of isolating trend values in a time series.
Use the information given below to find the P-value. Also, use a 0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to
For a distribution of scores with = 82 and standard deviation = 2.5, find the following: (Don't forget to sketch the normal curve to help you visualize what you are trying to fi
The box plot displays the diversity of data for the age; the data ranges from 19 being the minimum value and 60 being the maximum value. The box plot is positively skewed at 0.57 a
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