Chapter 10.3, Problem 1Q

Verify the following identity concerning the statistic of Theorem 10.3.1. Note that the right-hand side is more convenient for calculations.

${\displaystyle \underset{i=1}{\overset{t}{\sum }}\frac{{\left(X_i-n{p}_i\right)}^2}{n{p}_i}}={\displaystyle \underset{i=1}{\overset{t}{\sum }}\frac{X_i^2}{n{p}_i}}-n$