expected value of matrix

I have a random vector alpha with mean zero and standard deviation one, I want to find the expected value of alpha *alpha transpose

E[alpha*alpha']

0.0994

0.3661

-0.2125

0.2839

Answer 1

[VBBV]

 alpha = [0.0994
    0.3661
   -0.2125
    0.2839]

alpha = 4×1

0.0994 0.3661 -0.2125 0.2839

 alpha.' 

ans = 1×4

0.0994 0.3661 -0.2125 0.2839

 E = alpha.*alpha.'

E = 4×4

0.0099 0.0364 -0.0211 0.0282 0.0364 0.1340 -0.0778 0.1039 -0.0211 -0.0778 0.0452 -0.0603 0.0282 0.1039 -0.0603 0.0806

 Exp = mean(E)  % expected value 

Exp = 1×4

0.0133 0.0491 -0.0285 0.0381

Use mean function for your 4x4 matrix

[rakesh kumar]

Dear VBBV,

I have read that if alpha is a random vector then Expectation of [alpha*transpose(alpha)] gives covariance matrix which in this case should be a 4 by 4 matrix. yours answer calucalate the mean of column vector.

[VBBV]

Refer this link for expected value.

https://en.m.wikipedia.org/wiki/Expected_value

You can evaluate covariance using expected value. But your question is related to expected value (which is obtained by taking mean of values ) and not that of covariance.

Answer 2

[KSSV]

a = [  0.0994
    0.3661
   -0.2125
    0.2839] ;
E = a'*a

E = 0.2697

[rakesh kumar]

dear kssv i want to find the expected value of alpha* alpha transpose which is a matrix given below. I want the expected value of it.

alpha* alpha'= 0.0099 0.0364 -0.0211 0.0282

0.0364 0.1340 -0.0778 0.1039

-0.0211 -0.0778 0.0452 -0.0603

0.0282 0.1039 -0.0603 0.0806

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