How much you know about statistics?

Calculus Level pending

Can you recognize this structure? What is the value of it?

∫ − ∞ ∞ 1 2 π σ 2 e − 1 2 ( x − μ ) 2 σ 2 d x \int _{ -\infty }^{ \infty }{ \frac { 1 }{ \sqrt { 2\pi { \sigma }^{ 2 } } } e^{ -\frac { 1 }{ 2 } \frac { { (x-\mu ) }^{ 2 } }{ { \sigma }^{ 2 } } }dx }


The answer is 1.

Fer Duarte by Fer Duarte , 27, Mexico

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2 solutions

Kay Xspre
Oct 29, 2015

In relation to statistics, this integral is a representation of graph of normal distribution. The area under the curve will equal to 100%, or 1.

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Michael Mendrin
Oct 29, 2015

Definite integral of the Gaussian function. It appears in many, many other fields, including physics. Some which doesn't even have anything to do with statistics. Such as, for example, optics.

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