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).
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.