Let {X 1 , X 2 , X 3 , ..., X n , X n+1 } be IID sample from a normal population with mean u and standard deviation d, show that: Var(X n+1 - x -bar n ) = ((n+1)d 2 )/n Note: x -bar n is the sample...

Let {X₁, X₂, X₃, ..., X_n, X_n+1} be IID sample from a normal population with mean
u andstandard deviation d, show that:

Var(X_n+1
-
x-bar_n) = ((n+1)d²)/n

Note:
x-bar_n
is the sample mean, as I could not get the symbol; and d is the popolation standard deviaton as I could not get the symbol; also, d²
is the variance.