16N.1.AHL.TZ0.H_2

pestleMathematicsAAHLPaper 116N· sl-4-7-discrete-random-variablessource ↗

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 $X$ .

N16/5/MATHL/HP1/ENG/TZ0/02.a

[2]

Find the expected value of $X$ .

[2]

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

N16/5/MATHL/HP1/ENG/TZ0/02.a/M A1A1

Note: Award A1 for each correct row.

[2 marks]

${\text{E}}(X) = 1 \times \frac{1}{6} + 2 \times \frac{1}{3} + 4 \times \frac{1}{3} + 6 \times \frac{1}{6}$ (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]

Examiners’ report

[N/A]