Statistics Solutions

[Solved] Given ∫_-∞ ^∞ e^-x^2dx=√π , Calculate the exact value of ∫_-∞ ^∞ e^-(x-a)^2/bdx The k-th moment m_k of

Question: Given \(\int\limits_{-\infty }^{\infty }{{{e}^{-{{x}^{2}}}}dx}=\sqrt{\pi }\),

  1. Calculate the exact value of \(\int\limits_{-\infty }^{\infty }{{{e}^{-{{\left( x-a \right)}^{2}}/b}}dx}\)
  2. The k-th moment \({{m}_{k}}\) of the normal distribution is defined by
\[\int\limits_{-\infty }^{\infty }{{{x}^{k}}{{e}^{-{{x}^{2}}/2}}dx}\]

Find \({{m}_{2}}\) and \({{m}_{4}}\).

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Solution: The downloadable solution consists of 2 pages
Deliverable: Word Document


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