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Show that the ISB in a bin containing the origin of the double exponen-tial density, f(x) = exp(-|x|)/2, is O(h3); hence, the discontinuity in the derivative of f does not have any asymptotic eect on consistency. Compare when 0 and h/2 are bin edges. Formally, if f is the ordinary negative exponential density, R(f') is innite because of the jump at zero (integral of the square of the Dirac delta function at 0), but R(f') is well-dened for the double exponential.
Consider the exact MISE of a histogram when f = U(0; 1).
(a) If the mesh tk = kh is chosen where h = 1/m, show that MISE(m, n) = (m - 1)/n.
(b) If tk = (k + 1/2 )h with h = 1/m, show that
(c) Conclude that
Verify the inequalities for the adaptive MISE.
Find the optimal adaptive meshes for a skewed Beta density using a numerical optimization program.
We want to investigate the income data. In the Excel file Midterm Data.xls there is a tab labeled "Income Data 2006". The data in the tab is the income reported by 400 people in
Estimate the standard deviation of the process: Draw the X (bar) and R charts for the data given and give your comments about the process under study. Estimate the standard de
These techniques are applied when the rows and the columns of the data table represent the same units and when the measure is a disiance or a similarity. The goal of the analysis i
Scenario : Mrs dick's year 1s and 2s carried out a level-one science investigation to explain the changes in a particular plant over a period of time. As part of the investigation
Q. Find the inverse Laplace transform of Y (s) = s-4/s 2 + 4s + 13 +3s+5/s 2 - 2s -3. Q. Use the Laplace transform to solve the initial value problem y''+ y = cos(3t), y(0) =
Show that when h = h* for the histogram, the contribution to AMISE of the IV and ISB terms is asymptotically in the ratio 2:1. Compare the sensitivity of the AMISE(ch) in Equa
Explain the characteristics of business forecasting.
Meaning of Interpolation and Extrapolation Interpolation is a method of estimating the most probable missing figure on the basis of given data under certain assumptions. On t
Methods of Forecasting Various techniques which are generally used in business forecasting are as under: 1. Forecasting through the opinion of heads of department
The file Midterm Data.xls has a tab labeled "Income Data 2009". This data is collected income data from a sample of 400 people in 2009. Use a hypothesis test to see whether the av
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