"ούτω γάρ ειδέναι το σύνθετον υπολαμβάνομεν, όταν ειδώμεν εκ τίνων και πόσων εστίν …"

11 Jan

In [1, p. 61 exercise 3.5] we are asked to show that for the conditions of Problem [1, p. 60, exercise 3.4] the CR bound is

and further to give a statement about the efficiency of the sample mean estimator. read the conclusion >

and further to give a statement about the efficiency of the sample mean estimator. read the conclusion >

28 Dez

In [1, p. 60 exercise 3.4] we are asked to prove that the estimate

is an unbiased estimator, given are independent and identically distributed according to a distribution. Furthermore we are asked to also find the variance of the estimator. read the conclusion >

(1) |

is an unbiased estimator, given are independent and identically distributed according to a distribution. Furthermore we are asked to also find the variance of the estimator. read the conclusion >

4 Dez

In [1, p. 60 exercise 3.3] we are asked to prove that the complex multivariate Gaussian PDF reduces to the complex univariate Gaussian PDF if N=1.
read the conclusion >

8 Nov

In [1, p. 60 exercise 3.2] we are asked to proof by using the method of characteristic functions that the sum of squares of N independent and identically distributed N(0,1) random variables has a distribution. read the conclusion >

10 Okt

In [1, p. 60 exercise 3.1] a real random vector is given , which is distributed according to a multivatiate Gaussian PDF with zero mean and covariance matrix:

We are asked to find if where is given by the relation:

so that and are uncorrelated and hence independent. We are also asked to find the Cholesky decomposition of which expresses as , where is lower triangular with 1′s on the principal diagonal and is a diagonal matrix with positive diagonal elements. read the conclusion >

We are asked to find if where is given by the relation:

so that and are uncorrelated and hence independent. We are also asked to find the Cholesky decomposition of which expresses as , where is lower triangular with 1′s on the principal diagonal and is a diagonal matrix with positive diagonal elements. read the conclusion >