e. Perform a prediction(kriging) on a grid covering the area [0,2]x[0,2].  Plot the result.(0.5 mark)f. Explain the obtained plot.

(a) Estimate the area under the graph of f(x) = 2/x from x = 1 to x = 2 using four approximating rectangles and right endpoints. (Round your answer to four decimal places.) Sketch the graph and the rectangles. Is your estimate an underestimate or an overestimate?underestimateoverestimate    (b) Repeat part (a) using left endpoints. (Round your answer to four decimal places.

Plot points with top and bottom 5%  mean kriging variance (use different point shapes for top and bottom points).

a. Produce a sample variogram on the interval [0,1] using 20 bins.(0.5 mark)b. Fit the spherical variogram to the sample variogram by using ordinary least squares. Use the initial values (1, 0.5) and nugget = 0.5.(0.5 mark)c.   Consider the location (1, 0.5). Plot locations of the data in black and this location in red in the same image.(0.5 mark)d. Use the kriging method to compute the predicted value and the variance at the point (1, 0.5). Round the answers with 4 decimal places. (0.5 mark)e. Perform a prediction(kriging) on a grid covering the area [0,2]x[0,2].  Plot the result.(0.5 mark)f. Explain the obtained plot.(1 mark)g. To prepare your data for cross-validation, use the R commands> a <- as.data.frame(s256i$data)> s <- SpatialPointsDataFrame(s256i$coords, a, proj4string=CRS(projargs=as.character(NA)), match.ID=TRUE)> v.fit <- as.vgm.variomodel(ols.n)where ols.n is the variogram fitted by the ordinary least squares method.Cross-validate your model by using leave-one-out cross-validation and a bubble plot of the result.(0.5 mark)h. Explain the obtained plot.(1 mark)i. Cross-validate your model by using 10-fold  cross-validation and a bubble plot of the result. Explain the obtained plot. and differences with leave-one-out cross-validation from f and g.(1 mark)j. Optimize the monitoring network using the criterion of minimum mean kriging variances.  Which data point has the maximum mean kriging variance?(0.5 mark)

Use Simpson's Rule with 10 subintervals to estimate the area under the graph of y = 0.2x2 for −4 ≤ x ≤ 2.

The area of the figure bounded by y = x2 – 2x + 3 and the line tangent to it at M (2, 3) and y-axis is 8/k, where k is ____