1) Write down the explicit expressions of the joint p.d.f. of the following random variables: a) Independent real-valued Gaussian random variables A and B where A has the mean ma and the variance o, and B has the mean mg and the variance op. b) Real-valuednx 1 Gaussian random vector x with the mean vector m and the covariance matrix K. c) Two independent complex circular Gaussian random variables X1 and X2 where X1 has the mean m, and the variance o?, and X2 has the mean m2 and the variance o.

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1) Write down the explicit expressions of the joint p.d.f. of the following random variables:
a) Independent real-valued Gaussian random variables A and B where A has the mean
ma and the variance o, and B has the mean mg and the variance o.
b) Real-valued n x 1 Gaussian random vector x with the mean vector m and the
covariance matrix K.
c) Two independent complex circular Gaussian random variables X1 and X2 where X1
has the mean m, and the variance o, and X2 has the mean m2 and the variance o3.
Transcribed Image Text:1) Write down the explicit expressions of the joint p.d.f. of the following random variables: a) Independent real-valued Gaussian random variables A and B where A has the mean ma and the variance o, and B has the mean mg and the variance o. b) Real-valued n x 1 Gaussian random vector x with the mean vector m and the covariance matrix K. c) Two independent complex circular Gaussian random variables X1 and X2 where X1 has the mean m, and the variance o, and X2 has the mean m2 and the variance o3.
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