Revision as of 10:57, 20 March 2013

Practice Problem: Various Questions about a 2D Gaussian

Let

$ X=\left( \begin{array}{l} X_1\\ X_2 \end{array} \right) $

be a two-dimensional Gaussian random variable with mean $ \mu $ and standard deviation matrix $ \Sigma $ given by

$ \mu=\left( \begin{array}{c} -1\\ 2 \end{array} \right) , \Sigma=\left( \begin{array}{cc} 3 & 1 \\ 1 & 3 \end{array} \right) $

a) Write the pdf of X using matrix notation.

b) Write the pdf of X without matrix or vector.

c) Find the marginal pdf for $ X_1 $.

d) Find a matrix M such that the vector $ Y=M(X-\mu) $ consists of independent random variables.

e) Find the joint pdf of Y.

Share your answers below

You will receive feedback from your instructor and TA directly on this page. Other students are welcome to comment/discuss/point out mistakes/ask questions too!

Answer 1

Write it here.

Answer 2

Write it here.

Answer 3

Write it here.

Back to ECE302 Spring 2013 Prof. Boutin

Back to ECE302