题目
设随机变量Xsim B(10,0.5)，则E(X^2)=____.(请写成小数格式）
设随机变量$X\sim B\left(10,0.5\right)$，则$E(X^{2})=$____.(请写成小数格式）
题目解答
答案
$\because X\sim B\left(10,0.5\right)$，
$\therefore E\left(X\right)=10\times 0.5=5$，$D\left(X\right)=10\times 0.5\times \left(1-0.5\right)=2.5$，
$\because D\left(X\right)=E(X^{2})-\left[E\left(X\right)\right]^{2}$，
$\therefore E(X^{2})=D\left(X\right)+\left[E\left(X\right)\right]^{2}=2.5+25=27.5$.
故答案为：$27.5$.
$\therefore E\left(X\right)=10\times 0.5=5$，$D\left(X\right)=10\times 0.5\times \left(1-0.5\right)=2.5$，
$\because D\left(X\right)=E(X^{2})-\left[E\left(X\right)\right]^{2}$，
$\therefore E(X^{2})=D\left(X\right)+\left[E\left(X\right)\right]^{2}=2.5+25=27.5$.
故答案为：$27.5$.