Question: In probability and statistics, you learn about probability density functions associated with a random variable \(X\). They are functions \(f: \mathbf{R} \rightarrow \mathbf{R}\) such that (i) \(f(x) \geq 0\) for all \(x \in(-\infty, \infty)\) and (ii) \(\int_{-\infty}^{\infty} f(x) d x=1 .\) Determine the real number \(k\) so that

is a probability density function. That is, determine \(k\) so that

then given your \(k\), verify that \(f(x) \geq 0\) for all \(x \in(-\infty, \infty)\).

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