Statistical signal processing question

Hi everyone,

I'm a final year engineering student doing a bit of statistical signal
processing, and I have a pretty easy question for anyone that cares to
answer (stats isn't my strong point :) ). Ok, here goes:

"If x[k] = cos(kw_d + P) is a random process with P uniformly
distributed on [0,pi], then find an expression for the covariance
function"

I've gone about this by calculating:

EV{x{k1]x[k2]}, where EV stands for 'expected value'.

However, I'm a bit confused about how the expected value should be
calculated. If the you're doing the expected value of the function of
two random variables, then this is equal to the double integral over
infinity of the product of the function and the joint pdf. If the two
random vars are independant, then this is equal to the double integral
over infinity of the product of (the function, and the two pdfs). EG:

EV{XY} = int{ int{ X*Y*p_X*p_Y}} (assuming independance between X &
Y)

In the question above, is the random variable 'P' which corresponds to
the random process at time k1 different to the random variable 'P'
which corresponds to the random process at time k2? Although they have
the same statistical characteristics, I'm thinking that because they
correspond to different random variables(the distribution of the random
variable corresponding to the value of the random process at time k1
versus the distribution of the random variable corresponding to the
value of the process at time k2). However, the solutions to the
tutorial treats the two 'P' s as equal.

TIA

Taras

.

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