Complex sentence: This shows that the sample mean and sample variance are independent; this can also be show by Basu's theorem, and this property "characterizes" the normal distribution--for no other distribution are the sample mean and sample variance independent.
Split into simpler sentences: This shows that the sample mean and sample variance are independent. This can also be shown by Basu's theorem, and in fact this property "characterizes" the normal distribution--for no other distribution are the sample mean and sample variance independent.