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Probability density function (PDF) of a continuous random variable gives the relative probability for each of its possible values. Use this tag for discrete probability mass functions (PMFs) too.

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How to prove symmetry of a Uniform kernel?

I am trying to prove this kernel is valid, $$ K(x) = \frac{1}{2}I(-1 < x < 1) $$ So far I can integrate to 1, but how do I prove $$k(x) = k(-x)$$ Also, how do we satisfy that k(x) is $\ge$ 0 for all x …
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