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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.
what are the importance, uses,optimums and applications of the following in agriculture field experiments; 1.standard deviation 2.standard error 3. coefficient of variation
In a study of outcomes for patients who had been in the Intensive care Unit (ICU) at a large hospital, the records from last 150 patients who had been in the ICU for more than one
Show how the Normal bin width rule can be modi ed if f is skewed or kurtotic. Examine the eff ect of bimodality. Compare your rules to Doane's (1976) extensions of Sturges' rule.
If the data set contains an odd number of items, the middle item of the array is the median. If there is an even number of items, the median is the average of the two items. If the
Question: (a) A normal distribution is thought to have a mean of 50. A random sample of 100 gave a mean of 52.6 and a standard deviation of 14.5. A significance test was carri
Mean Absolute Deviation To avoid the problem of positive and negative deviations canceling out each other, we can use the Mean Absolute Deviation which is given by
You are attempting to purchase a part from a specialty vendor. Your company requires a C p of at least 1.67 on a critical dimension of the part. The dimensional specific
Factor analysis (FA) explains variability among observed random variables in terms of fewer unobserved random variables called factors. The observed variables are expressed in
Bernoulli's Theorem If a trial of an experiment can result in success with probability p and failure with probability q (i.e.1-p) the probability of exactly r success in n tri
Purposive or Judgement Sampling Under this method of sampling, the choice of selection of sample items from the universe depends exclusively on the judgement of the investi
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