Fatigue Evaluation of Riveted Railway Bridges" (J. of Bridge Engr, 2008: 237-244) suggested the exponential distribution with $\lambda = 0.19$ as a model for the distribution to four decimal places. (a) Find $E(X)$ by integrating $xf(x)$ from 0 to $\infty$. The integration by parts formula states
$f(x) = \begin{cases} 0.19 \exp(-0.19x) & \text{if } 0 \le x < \infty \\ 0 & \text{otherwise.} \end{cases}$
$\int_a^b u(x)v'(x)dx = u(x)v(x)|_a^b - \int_a^b u'(x)v(x)dx$.
bridge connection, determine the probability of the stress level being greater than 6, given that we already know the stress level is at least 4.