Mathematics: Let x be a uniform (0, 1) random variable. compute e[x n ] by using proposition 2.1, and then check the result by using the definition of expectation.

Let x be a uniform (0, 1) random variable. compute

tishfaco5000

11.01.2022

Assuming you're talking about the th moment, E[X^n] , we have by definition of expectation of a function of a random variable

$\displaystyle E[X^n]=\int_{-\infty}^\infty x^nf_X(x)\,\mathrm dx$

where f_X is the PDF for . The th moment for the standard uniform distribution is then

$\displaystyle\int_0^1 x^n\,\mathrm dx=\frac{x^{n+1}}{n+1}\bigg|_0^1=\boxed{\frac1{n+1}}$

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rustjallison9928

04.03.2021

ight among us time i guess

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