Moving Average and Time Series

Question

I just recently started to learn about moving average process of order 1, however, I get confused if there are other things attached to the equation.

1. For example: $Z_t = 8 + 2t + 5X_t$ where $X_t$ is a zero-mean stationary series with auto covariance function $r_k$

a) Find the mean function and the auto covariance function of $Z_t$

I am guessing:

Mean = $E[Z_t]=E[8+2t+5X_t]=E[8]+2E[t]+E[X_t]=0$

Covariance = $Cov[Z_t,Z_t]=E[Z_tZ_t]=E[8+2t+5X_t][8+2t+5X_t]=r_k^2$

Can someone please tell me if I did this correct?

2. The questions says X_t is a zero-mean, unit variance, stationary process with autocorrelation function $p_k$.

Then how do I find the mean, variance, and auto covariance of

$Z_t = 8 + 2t + 4t\,X_t$ ?

Mean = $E[Z_t]=E[8+2t+4tX_t]=E[8]+2E[t]+4tE[X_t]=0$ ?

Variance = No idea

Covariance = I guess I just have to use corr(x,x)=$cov(x,x)/\sqrt(var(x)var(x))$ ?