Deterministic Random Process: The Mean Value and Variance

Sample functions from a deterministic random process are described by

X(t)= At + B t>=0
= 0 t<0

where A is a Gaussian random variablewith zero meanand a varianceof 9 and B is a random variable that is uniformly distributed between 0 and 6. A and B are statistically independent.

A) Find the mean value of this process.

B) Find the variance of this process.

C) If a particular sample function is found to have a value of 10 at t=2 and a value of 20 at t=4, find the value of the sample function at t=8.

A) Find the mean value of this process.
E(X) = E(At + B) = AE(t) + B = A*0 + B = B

B)Find the variance of this process.
Var(X) …

This solution computes the mean value and variance of a deterministic random process where A is a Gaussian random variable and B is uniformly distributed.