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. They are also independent of L1L_1L1 and L2L_2L2. 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).
390 exam-style questions on OCR (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.