Question 4 - A-Level Maths

Exam Board	OCR
Module	Further Statistics AS (Further Statistics AS)
Year	2023
Session	June
Topic	Discrete Probability Distributions
Type	Two unknowns from sum and expectation

4 A discrete random variable \(W\) has the probability distribution shown in the following table, in which \(a\) and \(b\) are constants.

\(w\)	58	59	60	61	62	63
\(\mathrm { P } ( W = w )\)	\(a\)	\(b\)	0.2	0.2	0.1	0.1

It is given that \(\mathrm { E } ( W - 60 ) = 0.15\). Determine the value of \(\operatorname { Var } ( 4 W - 60 )\).