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Date May 2012 Marks available 6 Reference code 12M.1.sl.TZ2.4
Level SL only Paper 1 Time zone TZ2
Command term Find Question number 4 Adapted from N/A

Question

The random variable X has the following probability distribution, with \({\rm{P}}(X > 1) = 0.5\) .


 

Find the value of r .

[2]
a.

Given that \({\rm{E}}(X) = 1.4\) , find the value of p and of q .

[6]
b.

Markscheme

attempt to substitute \({\rm{P}}(X > 1) = 0.5\)     (M1)

e.g. \(r + 0.2 = 0.5\)

\(r = 0.3\)     A1     N2

[2 marks]

a.

correct substitution into \({\rm{E}}(X)\) (seen anywhere)     (A1)

e.g. \(0 \times p + 1 \times q + 2 \times r + 3 \times 0.2\)

correct equation     A1

e.g. \(q + 2 \times 0.3 + 3 \times 0.2 = 1.4\) , \(q + 1.2 = 1.4\)

\(q = 0.2\)     A1      N1

evidence of choosing \(\sum {{p_i} = 1} \)     M1

e.g. \(p + 0.2 + 0.3 + 0.2 = 1\) , \(p + q = 0.5\)

correct working     (A1)

\(p + 0.7 = 1\) , \(1 - 0.2 - 0.3 - 0.2\) , \(p + 0.2 = 0.5\)

\(p = 0.3\)     A1 N2

Note: Exception to the FT rule. Award FT marks on an incorrect value of q, even if q is an inappropriate value. Do not award the final A mark for an inappropriate value of p.

[6 marks]

b.

Examiners report

The majority of candidates were successful in earning full marks on this question.

a.

In part (b), a small number of candidates did not use the correct formula for \({\rm{E}}(X)\) , even though this formula is given in the formula booklet. There were also a few candidates who incorrectly assumed that \(p = 0\) , forgetting that the sum of the probabilities must equal 1. There were a few candidates who left this question blank, which raises concerns about whether they had been exposed to probability distributions during the course.

b.

Syllabus sections

Topic 5 - Statistics and probability » 5.7 » Concept of discrete random variables and their probability distributions.
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