Autocorelation of random process

G ,G′ and U are independant random variables. G and G′ are iid gausian and U is uniform [0,1].

If we have a random process Y(t) such trhat Y(t)=G if t>u

G′ if t≤u

Find the mean and autocorelation of the process Y(t)

The mean I can find, i am getting the wrong answer for the autocorelation, it is tricky because U is a random variable

Re: Autocorelation of random process

are G, G and U realised once or are they random processes G(t) G'(t) and U(t)?

Re: Autocorelation of random process

they are not random processes evolving in time

Re: Autocorelation of random process

can you find the conditional autocorrelation? if so, using the law of iterated expectations on the result.