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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.
1. Assume the random vector (Trunk Space, Length, Turning diameter) of Japanese car is normally distributed and the unbiased estimators for its mean and variance are the truth. For
In simple regression the dependent variable Y was assumed to be linearly related to a single variable X. In real life, however, we often find that a dependent variable may depend o
(i) Plot the step responses of the following second order systems and state the nature of each system. For each case, find the poles and plot the location of the poles in the compl
Explain what central tendency and variability are. In your answer define what the mean, median, mode, variance, and standard deviation are. What is the difference between the descr
What does the confidence level of a confidence interval tell you? Suppose that a population has mean, µ, and standard deviation, σ. What does the central limit theorem tell us
Waht is the product of £ x
Regression line drawn as Y=C+1075x, when x was 2, and y was 239, given that y intercept was 11. calculate the residual
While there are p original variables the number of principal components is m such that m
The following dataset is from a study of the effects of second hand smoking in Baltimore, MD, and Washington, DC. For the 25 children involved in this study the outcome variable is
Each weekend, Derek either reads a book (B), goes to the cinema (C), visits his local museum (M), or plays squash (S). If he reads a book one weekend, then he will take part in one
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