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Produce a discrete time series y(ti) by super positioning 5 cosinusoidal components,
for your own choice of the amplitudes (aj) and frequencies (fj).
Add some Gaussian noise to each digitised value. Experiment with amplitudes (including that of the noise term), and frequencies, showing results graphically. Then smooth your noisy time series with at least two different filters, e.g., a simple moving average smoother and an order two binomial filter.
Discuss the relative performance of the smoothers. You should consider quantifiable parameters such as; variance, r.m.s. deviations from the noise-free time series, and signal attenuation. Comment on the validity of the expression below, for your chosen smoother.
(i) Test for the existence of regression (the F-test). Carefully de ne the null and alternative hypothesis, and explain the result of any R output you obtain. (ii) Which of the
There is an illustration of a diesel engine sixteen cylinder that is supposed to be four-cycle, however GM never made engines of that size that were not two-cycle. The four valves
A house wall may be approximated as two 1.2 cm layers of fiber insulating board, a 8 cm layer of loosely packed asbestos, and 10 cm layer of common brick. Assuming convective heat
simple problems on partial derivatives
A researcher is interested in comparing the Christian maturity level of students who volunteer for community service versus those who do not. The researcher suppose that those who
Use Lagrange interpolation to estimate f(3), given that f(1) = 1, f(4) = -3, f(2) = 0 and f(-1) = 3.
A young couple requires RM30000 for an overseas trip which they want to make in six years time. How much they have to invest now at 18% p.a. compound interest compounded monthly, t
Prove that the Lagrangian coef?cient polynomials for p n (x) satisfy ∑ n k=0 l k (x) = 1. Hint: It is only a 3-line proof. Consider the interpolating polynomial for a constan
A scientist calculates the temperature of melting platinum using a new type of thermometer. The temperature of the metal is called to be exactly 1768.3 centigrade. The measurements
Let z 0 = a + ic, z 1 = b + id, z 2 = -id, and z = [z 0 + z 1 ]. Let z 0 be the apex of the wedge with one ray passing through z 1 and the other passing through z 2 , and
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