Question
State if the following is not the probability mass function of a random variable. Give reasons for your answer.
| X | $0$ | $1$ | $2$ |
| P(X) | $0.4$ | $0.4$ | $0.2$ |
| X | $0$ | $1$ | $2$ |
| P(X) | $0.4$ | $0.4$ | $0.2$ |
| X | $0$ | $1$ | $2$ |
| P(X) | $0.4$ | $0.4$ | $0.2$ |
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$\cot ^{-1}\left[\cot \left(e^{ x 2}\right)\right]$
$\frac{(1+\log x)^3}{x}$