A random variable ((xi)) is Poisson distributed; (mathbf{M} xi=lambda). Prove that as (lambda ightarrow infty), the distribution of the variable (frac{xi-lambda}{sqrt{lambda}}) tends to the

A random variable \((\xi)\) is Poisson distributed; \(\mathbf{M} \xi=\lambda\). Prove that as \(\lambda \rightarrow \infty\), the distribution of the variable \(\frac{\xi-\lambda}{\sqrt{\lambda}}\) tends to the normal law for which the parameters \(a\) and \(\sigma\) are \(a=0, \sigma=1\).