| Date | November 2016 | Marks available | 2 | Reference code | 16N.1.hl.TZ0.2 |
| Level | HL only | Paper | 1 | Time zone | TZ0 |
| Command term | Find | Question number | 2 | Adapted from | N/A |
Question
The faces of a fair six-sided die are numbered 1, 2, 2, 4, 4, 6. Let \(X\) be the discrete random variable that models the score obtained when this die is rolled.
Complete the probability distribution table for \(X\).
[2]
a.
Find the expected value of \(X\).
[2]
b.
Markscheme
A1A1
Note: Award A1 for each correct row.
[2 marks]
a.
\({\text{E}}(X) = 1 \times \frac{1}{6} + 2 \times \frac{1}{3} + 4 \times \frac{1}{3} + 6 \times \frac{1}{6}\) (M1)
\( = \frac{{19}}{6}{\text{ }}\left( { = 3\frac{1}{6}} \right)\) A1
Note: If the probabilities in (a) are not values between 0 and 1 or lead to \({\text{E}}(X) > 6\) award M1A0 to correct method using the incorrect probabilities; otherwise allow FT marks.
[2 marks]
b.
Examiners report
[N/A]
a.
[N/A]
b.
Syllabus sections
Topic 5 - Core: Statistics and probability » 5.5 » Concept of discrete and continuous random variables and their probability distributions.
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