Question: Losses, $X$, foloow a distribution with probability density function
1. The problem states that losses, denoted by $X$, follow a distribution with a probability density function (pdf).
2. To analyze or work with this distribution, we need the explicit form of the pdf, which is not provided in the prompt.
3. Generally, a pdf $f(x)$ satisfies two important rules:
- $f(x) \geq 0$ for all $x$ in the domain.
- The total area under the pdf curve equals 1, i.e., $$\int_{-\infty}^{\infty} f(x) \, dx = 1.$$
4. Without the explicit pdf, we cannot perform further calculations such as finding probabilities, expected value, or variance.
5. Please provide the explicit form of the pdf to proceed with detailed steps and calculations.