We have seen earlier that if X~ N(0, 2) and Y~ N(0, 0) are independent Gaussian...

Transcribed Image Text:

We have seen earlier that if X~ N(0, 2) and Y~ N(0, 0) are independent Gaussian random variables, then X + Y is a Gaussian random variable as well. Using induction, show that any linear combination of the components of an IID normalized Gaussian random vector W~N(0, In) is also a Gaussian random variable. (This exercise confirms that W is jointly Gaussian.) We have seen earlier that if X~ N(0, 2) and Y~ N(0, 0) are independent Gaussian random variables, then X + Y is a Gaussian random variable as well. Using induction, show that any linear combination of the components of an IID normalized Gaussian random vector W~N(0, In) is also a Gaussian random variable. (This exercise confirms that W is jointly Gaussian.)

Answer rating: 100% (QA)

The detailed ... View the full answer