Explanation

Let's analyze each option based on the properties of linear transformations:

Given: Y = A + BX, where B < 0 (decreasing linear transformation)

A. The mean of Y is identical to the mean of X.

• False: E[Y] = A + B·E[X], so the mean changes unless A = 0 and B = 1

B. The location shift of A has no effect on the variance of Y.

• True: V[Y] = B²·V[X], so variance depends only on B (the scaling factor), not on A (the location shift)

C. The skewness of Y is identical to the skewness of X.

• False: For B < 0, skewness has the same magnitude but opposite sign

D. The kurtosis is affected by decreasing linear transformations.

• False: Kurtosis is unaffected by linear transformations (both location and scale changes)

Therefore, only statement B is correct.