The independent random variables X X\,X and Y Y\,Y represent the lifespans, in thousands of hours, of two types of industrial cooling fans, where X∼N(60,52)X \sim N(60, 5^2)X∼N(60,52) and Y∼N(45,42)Y \sim N(45, 4^2)Y∼N(45,42). A system efficiency parameter, AAA, is defined by the linear combination
A=2X−2Y A = 2X - 2Y A=2X−2YFind:
E(A)E(A)E(A)
Var(A)Var(A)Var(A)
A batch of 5 independent fans of type X X\,X is tested. The random variable B B\,B is defined as the sum of their lifespans, B=∑i=15XiB = \sum_{i=1}^{5} X_iB=∑i=15Xi. Calculate the probability P(B>11A)P(B > 11A)P(B>11A).
