Mathematics Statistics 2 9709: Linear Combination Of Random Variables Topical Past Paper Questions

The random variable X has mean 2.4 and variance 3.1. 1ne random variable X has mean 2.4 and variance 5.1. (i) The random variable Y is the sum of four independent values of X. Find the mean and variance of Y. [2] (ii) The random variable Z is defined by $ Z = 4X - 3 $. Find the m…

The times, in months, taken by a builder to build two types of house, $P$ and $Q$, are represented by the independent variables $T_{1} \sim \mathrm{N}(2.2, 0.4^{2})$ and $T_{2} \sim \mathrm{N}(2.8, 0.5^{2})$ respectively. (i) Find the probability that the total time taken to buil…

The numbers of barrels of oil, in millions, extracted per day in two oil fields A and B are modelled by the independent random variables X and Y respectively, where $ X \sim \mathrm{N}(3.2, 0.4^{2}) $ and $ Y \sim \mathrm{N}(4.3, 0.6^{2}) $. The income generated by the oil from t…