Let Z_(1) and Z_(2) be independent standard normal random variables and U_(1)=Z_(1) and U_(2)=Z_(1)+Z_(2). Are U_(1) and U_(2) independent? Why?

Haiden Meyer

Haiden Meyer

Answered question


Let Z 1 and Z 2 be independent standard normal random variables and U 1 = Z 1 and U 2 = Z 1 + Z 2 . Are U 1 and U 2 independent? Why?

Answer & Explanation

Giancarlo Phelps

Giancarlo Phelps

Beginner2022-10-03Added 10 answers

C o v ( U 1 , U 2 ) = 1
For independent variables, we know that the covariance is zero.
Since the covariance between U 1 and U 2 is nonzero, it is then not possible that U 1 and U 2 Are independent.
Not independent, covariance nonzero.

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