Obliczenie prawdopodobieństwa

[zuku8818]

Niech X ma rozkład \(\displaystyle{ N(1,2)}\) .
Oblicz \(\displaystyle{ P(\frac{2X^{2}}{X^2+1}>1)}\)

z góry dziękuje

[bstq]

\(\displaystyle{ P\left(\frac{2X^{2}}{X^{2}+1}>1\right)=P\left(2X^{2}>X^{2}+1\right)=P\left(X^{2}>1\right)=1-P\left(X^{2}\le1\right)=1-P\left(\sqrt{X^{2}}\le\sqrt{1}\right)=1-P\left(|X|\le1\right)=1-P\left(-1\le X\le1\right)=1-P\left(-1\le X\le1\right)=1-0=1}\)

bo \(\displaystyle{ suppX=\left[1,2\right]}\)