题目

设服从参数为2的泊松分布，则 |X-2|leqslant dfrac {sqrt {2)}(2)} =( ) () |X-2|leqslant dfrac {sqrt {2)}(2)} =( ) () |X-2|leqslant dfrac {sqrt {2)}(2)} =( ) () |X-2|leqslant dfrac {sqrt {2)}(2)} =( ) () |X-2|leqslant dfrac {sqrt {2)}(2)} =( ) ()

设服从参数为2的泊松分布，则 $P\left\{\left|X-2\right|\le\frac{\sqrt{2}}{2}\right\}=\left(\ \ \ \right)$

$A.1-2e^{-2}$

$B.2e^{-2}$

$C.1-e^{-2}$

$D.e^{-2}$

题目解答

已知泊松分布服从参数为2，则其分布律为

$P\left(X=k\right)=\frac{2^k}{k!}e^{-2}\left(k=0,1,2,...\right)$

$P\left\{\left|X-2\right|\le\frac{\sqrt{2}}{2}\right\}=P\left\{\frac{4-\sqrt{2}}{2}\le X\le\frac{4+\sqrt{2}}{2}\right\}$

由 $k=\left(0,1,2,...\right)$

可得： $X=k=2$

故可得：

$P\left\{\left|X-2\right|\le\frac{\sqrt{2}}{2}\right\}=\frac{2^2}{2!}e^{-2}=2e^{-2}$

故本题的正确答案为 $B$