The independent random variables L1L_1L1 and L2L_2L2 represent the mechanical loads, in kN, applied to two different structural supports during a stress test. They are defined as L1∼N(140,42)L_1 \sim N(140, 4^2)L1∼N(140,42) and L2∼N(35,1.52)L_2 \sim N(35, 1.5^2)L2∼N(35,1.52). A differential stress index DDD is defined by the relation:
D=2L1−7L2 D = 2L_1 - 7L_2 D=2L1−7L2Find E(D)E(D)E(D).
Find Var(D)Var(D)Var(D).
The independent random variables L1,1,L1,2,…,L1,6L_{1,1}, L_{1,2}, \dots, L_{1,6}L1,1,L1,2,…,L1,6 each follow the same distribution as L1L_1L1. An aggregate load variable BBB is defined as:
B=∑i=16L1,i B = \sum_{i=1}^{6} L_{1,i} B=i=1∑6L1,iCalculate P(B>30D)P(B > 30D)P(B>30D).
