Question 2 - A-Level Maths

Exam Board	Edexcel
Module	S1 (Statistics 1)
Topic	Discrete Probability Distributions
Type	Two unknowns from sum and expectation

2. The discrete random variable \(X\) has the following probability distribution.

\(x\)	1	2	3	4	5
\(\mathrm { P } ( X = x )\)	\(a\)	\(b\)	\(\frac { 1 } { 4 }\)	\(2 a\)	\(\frac { 1 } { 8 }\)

Find an expression for \(b\) in terms of \(a\).
Find an expression for \(\mathrm { E } ( X )\) in terms of \(a\). Given that \(\mathrm { E } ( X ) = \frac { 45 } { 16 }\),
find the values of \(a\) and \(b\),