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If x and y are two independent random variables then their joint density function is given by
The density function fz of the sum of these two variables is given by the convolution
The proof of this relation may be found in any good introductory text on probability. According to the preceding exercise, if x and y are each U[0,1] then their joint density is triangular, i.e., t = rlr, using symbol t for triangle. What has the central limit theorem got to do with this process of repeated convolution?
If a temperature function is given in the x,y plane by T(x,y) = x+y, what is the value, to 3 decimal places, of the corresponding temperature function T1(u,v) at the point (u,v) =
simple problems on partial derivatives
At 8am particle A is at point (0,0) and moves horizontally to the right with constant velocity of 60km/hr. At the same time particle B is at the point (0, A+B+C+5) and moves horiz
i have a wav file which consists of a number of hammer impact noises. i want to break up each impact into and individual wav file. i want to ignore the first 40ms of the impact and
An open-loop control system has the following state-space model: (a) Find characteristic equation of the open-loop control system model. (b) What is the characteristic e
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
In an article in Marketing Science , Silk and Berndt investigate the output of advertising agencies. They describe ad agency output by finding the shares of dollar billing volume
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
Code and test Jacobi and Gauss-Sidel solvers for arbitrary diagonally dominant linear systems.
Given the loop transfer function G(s)H(s) = k/s(s+3)(s+4)(s+5) (a) Sketch the root locus plot for G(s)H(s). (b) What is the system gain at s = -1+ 2i? (c) Calculate the
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