9709 P52 - Nov 2023 - Q1 - 5 marks
2963
A competitor in a throwing event has three attempts to throw a ball as far as possible. The random variable \(X\) denotes the number of throws that exceed 30 metres. The probability distribution table for \(X\) is shown below.
| \(x\) | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| \(P(X=x)\) | 0.4 | \(p\) | \(r\) | 0.15 |
(a) Given that \(E(X)=1.1\), find the value of \(p\) and the value of \(r\). [3]
(b) Find the numerical value of \(\operatorname{Var}(X)\). [2]
