For f(x)=r(2v)πv r(2v+1)(1+vx2)−2v+1 where f(x) is the t-student probability function, determine its expected value and variance. Prove the result using the properties of the first and second derivative of the function.

We may use mathematics and the characteristics of the first and second derivatives to get the expect...

Resuelto For f(x)=r(2v)πv r(2v+1)(1+vx2)−2v+1 where f(x)

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Pregunta: For f(x)=r(2v)πv r(2v+1)(1+vx2)−2v+1 where f(x) is the t-student probability function, determine its expected value and variance. Prove the result using the properties of the first and second derivative of the function.
For f(x)=r(2v)πv r(2v+1)(1+vx2)−2v+1 where f(x) is the t-student probability function, determine its expected value and variance. Prove the result using the properties of the first and second derivative of the function.

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Texto de la transcripción de la imagen:

Para

f (x) = \frac{Γ ( \frac{v + 1}{2} )}{Γ ( \frac{v}{2} ) π v} (1 + \frac{x ^{2}}{v})^{- 2}

donde

f (x)

es la función de probabilidad t-student, determine su valor esperado y varianza. Demuestre el resultado utilizado las propledades de la primera y segunda derivada de la función.

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Pregunta: For f(x)=r(2v​)πv r(2v+1​)​(1+vx2​)−2v+1​ where f(x) is the t-student probability function, determine its expected value and variance. Prove the result using the properties of the first and second derivative of the function.

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Pregunta: For f(x)=r(2v)πv r(2v+1)(1+vx2)−2v+1 where f(x) is the t-student probability function, determine its expected value and variance. Prove the result using the properties of the first and second derivative of the function.