# Random vector mean and covariance

1. Feb 2, 2014

### cutesteph

1. The problem statement, all variables and given/known data

Random vector Y = [Y_1 Y_2 Y_3 …. Y_m]' where ' = transpose mean = u and and ∑ = covariance

Z = N_1 * Y_1 + N_2 * Y_2 + …. + N_m*Y_m all N are numbers

Find the covariance of Z

E[ (Y- E[Y] )(Y - E[Y] ) ] = E[YY'] -E[Y]E[Y]'= [N_1 N_2 .. N_m] [∑ - u^2 ….∑ -u^2] ' This seems incorrect.

2. Feb 3, 2014

### statdad

If you want the covariance of Z why do you look at the covariance of Y?

Think about this: your Z can be written as

$$Z = \begin{pmatrix} N_1 & N_2 & \cdots & N_m \end{pmatrix} % \begin{pmatrix} Y_1 \\ Y_2 \\ \vdots \\ Y_m \end{pmatrix}$$

so you should be able to use properties of expectations for random vectors to simplify your work.

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