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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 e ect on consistency. Compare when 0 and h/2 are bin edges. Formally, if f is the ordinary negative exponential density, R(f') is in nite because of the jump at zero (integral of the square of the Dirac delta function at 0), but R(f') is well-de ned 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.
In 120 tosses of a coin, 45 heads and 75 tails are observed. Is this a balanced coin? Use a=0.05. (Follow the basic steps of hypothesis testing)
(a) If one solves the ordinary differential equation using Euler's method find an expression for the local truncation error. (b) Using the result of (a) above what will
Analytical Approach We will illustrate this through an example. Example 1 A firm sells a product in a market with a few competitors. The average price charged by the
i need to solve couple questions on a data set ?
how to find mse from ssr table not the anova table
First we look at these charts assuming that we know both the mean and the standard deviation of the process, that is μ and σ . These values represent the acceptable values (bench
Uses Arithmetic mean is widely used because of the following reasons: Mean is the simplest average to understand and easy to compute. It
This box plot displays the diversity wfood; the data ranges from 0.05710 being the minimum value and 0.78900 being the maximum value. The box plot is slightly positively skewed at
Coefficient of Determination The coefficient of determination is given by r 2 i.e., the square of the correlation coefficient. It explains to what extent the variation
Regression Lines It has already been discussed that there are two regression lines and they show mutual relationship between two variable . The regression line Yon X gives th
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