[See Solution] The following is a density function: f(x)= 2xe^-x^2 x≥ 0 , 0 x<0 , Compute Pr (X≥ 0) Pr (1≤ X≤ 2) Pr (X≤


Question: The following is a density function:

\[f\left( x \right)=\left\{ \begin{aligned} & 2x{{e}^{-{{x}^{2}}}}\,\,\,\,\,\,\,\,\,\,\,x\ge 0 \\ & 0\text{ }x<0 \\ \end{aligned} \right.\]

Compute

  1. \(\Pr \left( X\ge 0 \right)\)
  2. \(\Pr \left( 1\le X\le 2 \right)\)
  3. \(\Pr \left( X\le 2 \right)\)

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