| Date | May 2010 | Marks available | 6 | Reference code | 10M.2.hl.TZ2.2 |
| Level | HL only | Paper | 2 | Time zone | TZ2 |
| Command term | Calculate and Determine | Question number | 2 | Adapted from | N/A |
Question
A discrete random variable X has a probability distribution given in the following table.
(a) \({\text{E}}(X) = 2.61\), determine the value of p and of q.
(b) Calculate \({\text{Var}}(X)\) to three significant figures.
Markscheme
(a) \(p + q = 0.44\) A1
\(2.5p + 3.5q = 1.25\) (M1)A1
\(p = 0.29,{\text{ }}q = 0.15\) A1
(b) use of \({\text{Var}}(X) = {\text{E}}({X^2}) - {\text{E}}{(X)^2}\) (M1)
\({\text{Var}}(X) = 2.10\) A1
[6 marks]
Examiners report
An easy question, well answered by most candidates. For the others it was disappointing that many did not use the fact that the probabilities add to unity.
