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An experiment conducted over time T necessarily produces a windowed view of the phenomenon generating the data. It is a useful strategy to regard the windowed data as one period of a periodic function. Then one may write
and seek to calculate the Fourier coefficients cn from the integral expression
Large values of cn will be regarded as a quantitative indication of a genuine periodic change in the phenomenon under study. In digital form the relevant equations are
The time interval [0,T] has been marked out in equal steps T/N, and frequency fn = n/T has been replaced by the dimensionless quantity n/N.
what are the applications of integration?
(i) Test for the existence of regression (the F-test). Carefully dene the null and alternative hypothesis, and explain the result of any R output you obtain. (ii) Which of the
Ah Fong borrow RM10 000. The yearly simple interest rate is 10.5%, payable monthly, and the monthly payment is RM200. How much of the 1st payment goes to interest and how much to p
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
If x and y are two independent random variables then their joint density function is given by The density function f z of the sum of these two variables is given by the c
Valid objective function for a LPP with x,y,z as decision variables
The integral has an exact answer, viz., sinc(pfT). As T®¥ the sinc function tends to zero. Divide the region from -T/2 to T/2 into N equal parts and sum the rectangles on b
An auto manufacturing company wanted to investigate how the price of one of its car models depreciates with age. The research department at the company took a sample of eight cars
The displacement x meters of a mass from a fixed point about which it is oscillating is given by x=2.3cos?10pt+4.2sin?10pt where t is the time in seconds Express the displaceme
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
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