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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?
a. Explain the Integrated Circuits? What are the benefits of ICs as compared to standard printed circuits? b. Explain in brief, the various steps included in fabrication of ICs.
(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
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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
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
A function f(t) is defined as f(t) = p - t for 0 Write down the even extension of f(t) for -p Determine the Fourier cosine series, and hence, calculate the Fourier series approx
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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
What are the lowest and highest addresses in a 2 20 byte memory in which a four-byte word is the smallest addressable unit?
prove that A=3i+j-2k ,B= -i+3j+4k, C=4i-2j-6k can form a triangle and find the length of the medians of the triangle.
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