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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.
Variance The term variance was used to describe the square of the standard deviation by R.A.Fisher. The concept of variance is highly important in areas where it is possible to
Regression Coefficient While analysing regression in two related series, we calculate their regression coefficients also. There are two regression coefficients like two regress
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
The box plot displays the diversity of data for the totexp; the data ranges from 30 being the minimum value and 390 being the maximum value. The box plot is positively skewed at 1.
A) The three images shown below were blurred using square masks of sizes n=23, 25, and 45, respectively. The vertical bars on the le_ lower part of (a) and (c) are blurred, but a c
entropy test to measure interaction between enviornmental factors and genes
(a) The Horton's initial infiltration capacity for a catchment is 204 mm/h and the constant infiltration value at saturation is 60 mm/h. For a rainfall in excess of 204 mm/h mainta
You will recall the function pnorm() from lectures. Using this, or otherwise, Dteremine the probability of a standard Gaussian random variable exceeding 1.3. Using table(), or
#In planning the teaching assignments for next semester, Mr. Hinton must have a teacher in each of the 7 grades during each of the 6 periods of the day. If he has 10 teachers to ch
b. A paper mill produces two grades of paper viz., X and Y. Because of raw material restrictions, it cannot produce more than 400 tons of grade X paper and 300 tons of grade Y
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