Random variables $X,Y,Z$ have $0$ expectation and variance $\sigma^2$. Also, they are not correlated in pairs. Find maximum and minimum of $\mathbb{E}XYZ$
$\operatorname{cov}XY,Z=\mathbb{E}XYZ-\mathbb{E}XY\mathbb{E}Z=\mathbb{E}XYZ$
By Coshi-Bynakovsky inequality $cov^2(XY,Z)\leq DXYDZ=\sigma^2DXY$
$DXY=\mathbb{E}X^2Y^2-(\mathbb{E}XY)^2=\mathbb{E}X^2Y^2-(\operatorname{cov}X,Y+\mathbb{E}X\mathbb{E}Y)^2=\mathbb{E}X^2Y^2$
But then I stucked. How can bound $\mathbb{E}X^2Y^2?$