CAIE S2 2018 June — Question 2

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2018
SessionJune
TopicLinear combinations of normal random variables
TypeDistribution of linear combination

2 The random variable \(X\) has the distribution \(\mathrm { N } ( 3,1.2 )\). The random variable \(A\) is defined by \(A = 2 X\). The random variable \(B\) is defined by \(B = X _ { 1 } + X _ { 2 }\), where \(X _ { 1 }\) and \(X _ { 2 }\) are independent random values of \(X\). Describe fully the distribution of \(A\) and the distribution of \(B\). Distribution of \(A\) : \(\_\_\_\_\)
Distribution of \(B\) : \(\_\_\_\_\)