18M.1.AHL.TZ2.H_3

pestleMathematicsAIHLPaper 118M· sl-4-1-concepts-reliability-and-sampling-techniquessource ↗

The discrete random variable X has the following probability distribution, where p is a constant.

Find the value of p.

[2]

Find μ, the expected value of X.

[2]

b.i.

Find P(X > μ).

[2]

b.ii.

Markscheme / solution

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

equating sum of probabilities to 1 (p + 0.5 − p + 0.25 + 0.125 + p³ = 1) M1

p³ = 0.125 = $\frac{1}{8}$

p= 0.5 A1

[2 marks]

μ = 0 × 0.5 + 1 × 0 + 2 × 0.25 + 3 × 0.125 + 4 × 0.125 M1

= 1.375 $\left( { = \frac{{11}}{8}} \right)$ A1

[2 marks]

b.i.

P(X > μ) = P(X = 2) + P(X = 3) + P(X = 4) (M1)

= 0.5 A1

Note: Do not award follow through A marks in (b)(i) from an incorrect value of p.

Note: Award M marks in both (b)(i) and (b)(ii) provided no negative probabilities, and provided a numerical value for μ has been found.

[2 marks]

b.ii.

Examiners’ report

[N/A]

b.i.

[N/A]

b.ii.