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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?
The two sides of a triangle are 17 cm and 28 cm long, and the length of the median drawn to the third side is equal to 19.5 cm. Find the distance from an endpoint of this median to
With the help of energy bands explain how conduction takes place in semiconductors. Semiconductors: Substances as carbon, germanium and silicon that electrical conductivity l
model an equation to determine the amount of oil in a reservior
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
y''(x)=2*10^-6*y(x)(100000-y(x))
(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
A manager has determined the cost C, in dollars, for manufacturing is C(q) =85log 10 (10+q/2) for manufacturing, where q is the number of units produced in a given day. (a
trigonometric functions
P=(Fv- ? Av3) (1-e-µ?) P is Power v is velocity of the belt ? is the density of the belt material ? = 1200 kg/m3 A is the cross sectional a
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
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