## Definition A ==Loss Random Variable== (denoted $X$) represents the total financial loss arising from an insurable event before any policy adjustments are applied. It is the "raw" amount of damage or cost. The distribution of $X$ characterizes the frequency and severity of potential losses. > [!example]- Losses follow an exponential distribution with mean $\$2{,}000$. What is the probability a loss exceeds $\$5{,}000$? > For an exponential with mean $\mu = 2000$, the survival function is $P(X > x) = e^{-x/\mu}$. > $ P(X > 5000) = e^{-5000/2000} = e^{-2.5} \approx 0.0821 $