Consider a function \({f_X}\left( x \right) = \frac{k}{{{x^2}}}u\left( {x - k} \right)\) where u(x) is the unit step function.

This function will be a valid probability density function, for

1
k = 0
2
k to be an even number
3
k to be an odd number
4
Any non-zero value of k

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