Explanation

Let's analyze each option:

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

• Incorrect: From the linear transformation formula: $E[Y] = A + BE[X]$
• Since $A \neq 0$ and $B \neq 1$, the mean of Y is different from the mean of X

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

• Correct: Variance formula: $V[Y] = B^2V[X]$
• The variance depends only on $B^2$, not on the location shift parameter $A$
• This is a fundamental property of variance - location shifts don't affect dispersion

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

• Incorrect: When $B < 0$ (decreasing transformation), skewness has the same magnitude but opposite sign
• Since X follows a normal distribution, its skewness is 0, so Y's skewness would also be 0
• However, the statement is technically incorrect because it doesn't account for the sign change

D. The kurtosis is affected by decreasing linear transformations.

• Incorrect: Kurtosis is unaffected by linear transformations (both increasing and decreasing)
• For normal distributions, kurtosis remains 3 regardless of linear transformations

Key Insight: For linear transformations $Y = A + BX$:

• Mean: $E[Y] = A + BE[X]$
• Variance: $V[Y] = B^2V[X]$ (location shift A has no effect)
• Skewness: Same magnitude, sign changes if $B < 0$
• Kurtosis: Unaffected by linear transformations