Can someone give me an example where we have [tex]\mathbb{E}z=0 [/tex], [tex]\mathbb{E}z^2=1 [/tex] (i.e. finite expectations)(adsbygoogle = window.adsbygoogle || []).push({});

BUT,

[tex]\mathbb{E}z^4= \infty [/tex] ?

Also, I cannot think of a case where:

[tex]\mathbb{E}x=\infty [/tex] where [tex]x>0[/tex]

BUT,

[tex]\mathbb{E}| \log x |< \infty [/tex]

Thanks in advance

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# Example where higher moments are infinite

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