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Date May 2018 Marks available 2 Reference code 18M.1.AHL.TZ2.H_3
Level Additional Higher Level Paper Paper 1 (without calculator) Time zone Time zone 2
Command term Find Question number H_3 Adapted from N/A

Question

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

Find the value of p.

[2]
a.

Find μ, the expected value of X.

[2]
b.i.

Find P(X > μ).

[2]
b.ii.

Markscheme

* 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 =  1 8

p= 0.5      A1

[2 marks]

a.

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

= 1.375  ( = 11 8 )      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]
a.
[N/A]
b.i.
[N/A]
b.ii.

Syllabus sections

Topic 4—Statistics and probability » SL 4.3—Mean, median, mode. Mean of grouped data, standard deviation. Quartiles, IQR
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Topic 4—Statistics and probability » SL 4.7—Discrete random variables
Topic 4—Statistics and probability

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