PROBLEMS

Basic Random Processes

6.1 Suppose the sample space representing a random process is and let for . For equally likely ζ, specify the probability space for the random variables at t = 1 and t = 2, and sketch all realizations.

6.2 Let the sample space representing a random process be such that for . For uniformly distributed ζ, give the pdfs for the random variables at t = 2 and t = 4.

6.3 Consider the following random process which increases linearly with time:

(6.229) Numbered Display Equation

where a is a constant and X is uniformly distributed on [−1, 1]. Find the cdf and pdf Y(t) of for .

6.4 Let X(t

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