The correct answer is B. 1.
A probability density function (PDF) is a function that gives the probability of a random variable taking on a value within a given interval. The PDF is always non-negative and integrates to 1 over the entire real line.
In this case, the PDF is given by
$$p(x) = K e^{-\alpha |x|}, \quad x \in (-\infty, \infty)$$
The value of $K$ can be found by integrating the PDF over the entire real line. This gives
$$1 = \int_{-\infty}^{\infty} p(x) dx = K \int_{-\infty}^{\infty} e^{-\alpha |x|} dx = K \left[ \frac{1}{2 \alpha} e^{-\alpha |x|} \right]_{-\infty}^{\infty} = K$$
Therefore, $K = 1$.
The other options are incorrect because they do not satisfy the condition that the PDF integrates to 1 over the entire real line.