Problem $4$:

Let $Y1,Y2,Y3,$cdots.. be a sequence of independent non$-$identical random variables with mean $E[Yi]=0,$ and Var$(Yi)={}_i^2.$ For deterministic variables $c_i,$ we define the discrete$-$

time random process as

$x(n)=c_1{Y}_1+c_2{Y}_2$dots$+c_n{Y}_n,n=1,2,3,$dots,$N$

Now, we define a column vector $x=[x(1),x(2),....,x(N){]}^T$

Find the mean vector $m_x,$ correlation matrix $Rx,$ and covariance matrix $Cx$ for random vector X