The independent random variables XXX and YYY are defined as X∼N(50,42)X \sim N(50, 4^2)X∼N(50,42) and Y∼N(40,52)Y \sim N(40, 5^2)Y∼N(40,52). The random variable AAA is defined as
A=3X−2Y A = 3X - 2Y A=3X−2YFind:
E(A)E(A)E(A)
Var(A)Var(A)Var(A)
The random variables X1,X2,X3,X4,X5X_1, X_2, X_3, X_4, X_5X1,X2,X3,X4,X5 are independent of one another and of XXX and YYY, and each has the same distribution as XXX. The random variable BBB is defined as
B=∑i=15Xi B = \sum_{i=1}^{5} X_i B=i=1∑5XiFind P(B>4A)P(B > 4A)P(B>4A).