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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?
Produce a discrete time series y(t i ) by super positioning 5 cosinusoidal components, for your own choice of the amplitudes (a j ) and frequencies (f j ). Add some Gaus
You are working as an engineer on a project that involved being able to accurately measure the fluid level change in a large outdoor holding tank. The fluid level rises and falls a
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
can you tell me what is the physical intrepetation of convolution theorm or convolution integral?
An electronic module is mounted on a machine and is modelled as a single degree of freedom spring, mass, and damper. During normal operation, the module of mass m kg is subject to
Below are the conditions specified by the institution: a) If the temperature sensor shows 30 degree Celsius or higher, the air-conditioner will be turned ON regardless of the othe
(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
Ask question #how to identify region of the integral sum#
The data of the table below give details of the components, prices and standard quantities used in making a kind of chemical. Measure the composite index with 2007 as base year us
In the x,y plane, divide up the x-axis by placing marks at x=a, x=b, and x = -2. Suppose φ is harmonic in the upper half plane and on the segments of the x-axis defined by your mar
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