What is the variance of the difference between two successive signal

1.	What is the variance of the difference between two successive signal samples, d(n) = x(n) – x(n-1)?
A.	$σ_d^2=2σ_x^2 [1+γ_{xx} (1)]$
B.	$σ_d^2=2σ_x^2 [1-γ_{xx} (1)]$
C.	$σ_d^2=4σ_x^2 [1-γ_{xx} (1)]$
D.	$σ_d^2=3σ_x^2 [1-γ_{xx} (1)]$
Answer» C. $σ_d^2=4σ_x^2 [1-γ_{xx} (1)]$

Discussion

1.	What is the variance of the difference between two successive signal samples, d(n) = x(n) – x(n-1)?
A.	\(σ_d^2=2σ_x^2 [1+γ_{xx} (1)]\)
B.	\(σ_d^2=2σ_x^2 [1-γ_{xx} (1)]\)
C.	\(σ_d^2=4σ_x^2 [1-γ_{xx} (1)]\)
D.	\(σ_d^2=3σ_x^2 [1-γ_{xx} (1)]\)
Answer» C. \(σ_d^2=4σ_x^2 [1-γ_{xx} (1)]\)