Figure 7.5 shows the probability density function (PDF) of a generic triangular distribution with support \(\left(\begin{array}{ll}a, & b\end{array}\right)\) and mode \(c\). For such a distribution, expected value and variance are given by the following formulas:

Say that the profit from a financial portfolio, with a holding period of a few weeks, has a triangular distribution with parameters (in €) \(a=75,000, b=\) 55,000 , and \(c=40,000\), so that the maximum possible loss is \(€ 75,000\). Find \(\mathrm{V} @ \mathrm{R}\) at level \(95 \%\).The drawing of Fig. 7.5 is not in scale and is just meant as a qualitative hint.

Data From Figure 7.5

Transcribed Image Text:

E[X] = Var(x) = a+b+c 3 a2+b2c2-ab- ac -bc 18 -