Probability Density function

Question

Comments

m getting 0 as answer

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0.03125

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explain.

I'm getting this :

$\frac{1}{4}\left ( \frac{1}{16} - \frac{1}{16}\right ) = 0$

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o sorry o is correct

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I am also getting 0.

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why not 0.03125

Answer 1

$\int_{-\frac{1}{2}}^{\frac{1}{2}} f(x)dx$

$\int_{-\frac{1}{2}}^{\frac{1}{2}} x^{3}dx$

$\lim_{x->\frac{1}{2}}\left [ \frac{x^{4}}{4} \right ] - \lim_{x->-\frac{1}{2}}\left [ \frac{x^{4}}{4} \right ]$

= $\frac{1}{4}\left ( \frac{1}{16} - \frac{1}{16} \right )=0$

Comments

$\int_{-\frac{1}{2}}^{\frac{1}{2}} x^{3}dx$
=2 $\int_{\frac{0}{}}^{\frac{1}{2}} x^{3}dx$

=0.03125

is not it?

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This property is applicable when f(x) is even but here it is odd.