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Sample Functions: The Mean Value of the Random Variable

The random number generator in a computer generates three-digit numbers that are uniformly distributed between 0.000 and 0.999 at at rate of one random number per second starting at t=0. A sample function from a random process is generated by summing the 10 most recent random numbers and assigning this sum as the value of the sample function during each 1 second time interval. The sample functions are denoted as X(t) for t>=0.

A) Find the mean value of the random variable X(4.5).
B) Find the mean value of the random variable X(9.5).
C) Find the mean value of the random variable X(20.5)

Solution Preview

A) The random variable we have is X(4.5), which means that a sample function from a random process is generated by summing 45(4.5*10 ie,for 1 second the random numbers are 10 then for 4.5 seconds means 4.5*10) most recent random numbers and assigning this sum as the value of the sample function during each 4.5 second time interval.
The mean of ...

Solution Summary

This response calculates the mean value of the random variable within a sample function.

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