Question 3 - A-Level Maths

Exam Board	OCR MEI
Module	Further Statistics Major (Further Statistics Major)
Year	2022
Session	June
Topic	Discrete Probability Distributions
Type	Two unknowns from sum and expectation

3 The table shows the probability distribution of the random variable \(X\), where \(a\) and \(b\) are constants.

\(r\)	0	1	2	3	4
\(\mathrm { P } ( X = r )\)	\(a\)	\(b\)	0.24	0.32	\(b ^ { 2 }\)

Given that \(\mathrm { E } ( X ) = 1.8\), determine the values of \(a\) and \(b\). The random variable \(Y\) is given by \(Y = 10 - 3 X\).
Using the values of \(a\) and \(b\) which you found in part (a), find each of the following.
- \(\mathrm { E } ( Y )\)
- \(\operatorname { Var } ( Y )\)