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Sample Functions: The Mean Value of the Random Variable

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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)

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

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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 ...

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