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Date November 2017 Marks available 1 Reference code 17N.2.sl.TZ0.4
Level SL only Paper 2 Time zone TZ0
Command term Write down Question number 4 Adapted from N/A

Question

A discrete random variable \(X\) has the following probability distribution.

N17/5/MATME/SP2/ENG/TZ0/04

Find the value of \(k\).

[4]
a.

Write down \({\text{P}}(X = 2)\).

[1]
b.

Find \({\text{P}}(X = 2|X > 0)\).

[3]
c.

Markscheme

valid approach     (M1)

eg\(\,\,\,\,\,\)total probability = 1

correct equation     (A1)

eg\(\,\,\,\,\,\)\(0.475 + 2{k^2} + \frac{k}{{10}} + 6{k^2} = 1,{\text{ }}8{k^2} + 0.1k - 0.525 = 0\)

\(k = 0.25\)     A2     N3

[4 marks]

a.

\({\text{P}}(X = 2) = 0.025\)     A1     N1

[1 mark]

b.

valid approach for finding \({\text{P}}(X > 0)\)     (M1)

eg\(\,\,\,\,\,\)\(1 - 0.475,{\text{ }}2({0.25^2}) + 0.025 + 6({0.25^2}),{\text{ }}1 - {\text{P}}(X = 0),{\text{ }}2{k^2} + \frac{k}{{10}} + 6{k^2}\)

correct substitution into formula for conditional probability     (A1)

eg\(\,\,\,\,\,\)\(\frac{{0.025}}{{1 - 0.475}},{\text{ }}\frac{{0.025}}{{0.525}}\)

0.0476190

\({\text{P}}(X = 2|X > 0) = \frac{1}{{21}}\) (exact), 0.0476     A1     N2

[3 marks]

c.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.

Syllabus sections

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