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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?
This is a pen and paper exercise, you are expected to provide a detailed derivation. Follow the procedure outlined in the lectures for construction of a simple averaging by thr
In closed system 0.3kg of gas at 373K is expanded isothermally and reversibly from 1 mpa pressure to 200 kp. Given that cv= 718 j/kg k and R= 287 j/kgk.
a wire of 3mm diameter and 5 m long has a load of 100g suddenly applied to its ends. calculate stress and extension produced. also show that these are twice the static values
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
In the case of Castenedav . Partida , it was found that during a period of 11 years in Hilda County, Texas, 870 people were selected for grand jury duty, and 39% of them were Ame
simple problems on partial derivatives
Compute the (real and imaginary parts of the) principal value of the eighth root of (a + ib) to 3 decimal places (accurate to 10 -3 ). Call the real part "m 7 ", and the imagina
A stone weighing 50 newton is tied to one end of a cord 0.90 meter long. the stone is then whirled in a vertical circle. if the breaking strength of the cord in tension is 60 newto
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A cosmetic store offer at RM245 for a package, consisting of a foundation, a compact powder and a lipstick, which is saving of 15% on the cost of buying the units indiviually. If b
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