Question
State which of the following are not the probability mass function of a random variable. Give reasons for your answer : 


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$\cot ^{-1}\left(4^x\right.$
$\int_0^1 \frac{x^2-2}{x^2+1} \cdot d x$
$\frac{\left(\sin ^{-1} x\right)^{\frac{3}{2}}}{\sqrt{1-x^2}}$
$\sin ^{-1}\left(\frac{1}{2}\right)$