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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?
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
1. Joe and Sam each invested $20,000 in the stock market. Joe's investment increased in value by 5% per year for 10 years. Sam's investment decreased in value by 5% for 5 years and
Solve the initial value problem 11(t+1)dydt-7y=28t, for t>-1 with y(0)=14. Put the problem in standard form. Then find the integrating factor, ?(t)= , and finally find y(t)=
Verify how long $400 must be left to store at 12 % p.a. compounded monthly for it to amount to triple the soted value of another $400 deposited at the similar time at 8.8% p.a. com
y''(x)=2*10^-6*y(x)(100000-y(x))
A new gantry crane for a metal fabrication shop is to be designed. The designer has proposed the following two different configurations: A. Using only truss elements B. Using the
(13x7y)0
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
Two boys A and B are at two diametrically opposite points on a circle. At one instant the two start running on the circle; A anticlockwise with constant speed v and B clockwise wit
sin2+cos2=
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