
3.18. The time duration T of a force acting on a structure is a random variable having the probability
density function,
f
T
(t) =
αt
2
, 0 ≤ t ≤ 12
β, 12 ≤ t ≤ 16
0, elsewhere.
(a) Determine the appropriate values for constants a and b.
(b) Calculate the mean value and variance of T.
(c) Calculate Pr(T ≥ 6).
Solution: (a) Determine the appropriate values for constants a and b.
The cumulative distribut ...