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ne 10. 2019 4. A random process Z(t) is given by, Z(t) = Kt, where K is a random variable The probability dessity function fo

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Here Z(t)= Kt is random process and K is random variable so t is fixed. Mean can be computed using following equation,

fK (k)ktdk fR(k)Z(t)dk = _ - { ()z}3

(2/3 2)ktdk t(2/3k - k3)dk

k4 - -0 t[3k2 4 1

Autocovariance:

z(t, t) E{kt kt} - E(ktt)ttEk

  K2(2/3 k2)dk tt(2/3k2-k dk tit2

  k5 4 2 2 3 45 5

This is not wide sense stationary process because autocovariance function is not of the form

F(G t2 1 and because of that any difference it will change the value of autocovariance.

A process is wide sense stationary if

E{X(t)c for all t and z{t. t2)=r(t-t) for all t1 and t2

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