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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.
A file on DocDepot in the assignments folder on doc-depot called bmi.mtp contains data on the Body Mass Index (BMI) of a population of Ottawa residents. The first column identifies
1 A penny is tossed 5 times. a. Find the chance that the 5th toss is a head b. Find the chance that the 5th toss is a head, given the first 4 are tails.
in a normal distribution with a mean of 85 and a STD of 5, what is the percentage of scores between 75 and 90?
Introduction to Probability A student is considering whether she should enroll in an MBA educational program offered by a well-known college. Among othe
Characteristics of Index Number On the analysis of various definitions of index number the following may be its characteristics: 1. Expressed in Number : Index number
The following are the various types of common averages used in statistical analysis given in the form of a chart. Figure 1
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
As one of the oldest multivariate statistical methods of data reduction, Principal Component Analysis (PCA)simplifies a dataset by producing a small number of derived
Let X 1 and X 2 be two independent populations with population means μ 1 and μ 2 respectively. Two samples are taken, one from each population, of sizes n 1 and n 2 re
Calculation for Discrete Series or Ungrouped Data The formula for computing mean is = where, f = fr
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