Rewriting $\prod_{i=1}^{n}\frac{x_i}{(1+x_i)^2}$ as $\frac{\prod_{i=1}^{n}x_i}{\prod_{i=1}^{n}(1+x_i)^2}$

Question

Can we rewrite

$$\prod_{i=1}^{n}\frac{x_i}{(1+x_i)^2}$$

as

$$\frac{\prod_{i=1}^{n}x_i}{\prod_{i=1}^{n}(1+x_i)^2}$$

?

The product is commutative, hence you can rearrange a finite product in any way you like. — Jack D'Aurizio, Mar 18 '15 at 13:45
@aGer to find minimal sufficient statistic for logistic distribution , i need to rewrite a product term . — ABC, Mar 18 '15 at 13:53

score 11 · Accepted Answer · answered Mar 18 '15 at 13:45

11

Yes you can because $\frac AB\times\frac CD=\frac{AC}{BD}$.

answered Mar 18 '15 at 13:45

please delete me

1 Answers1