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Date November 2019 Marks available 6 Reference code 19N.2.SL.TZ0.S_7
Level Standard Level Paper Paper 2 Time zone Time zone 0
Command term Find Question number S_7 Adapted from N/A

Question

The following table shows the probability distribution of a discrete random variable X, where a0 and b0.

Show that b=0.3a.

[1]
a.

Find the difference between the greatest possible expected value and the least possible expected value.

[6]
b.

Markscheme

correct approach  A1

eg       0.2+0.5+b+a=1,  0.7+a+b=1

b=0.3a       AG  N0

[1 mark]

a.

correct substitution into E(X)        (A1)

eg       0.2+4×0.5+a×b+(a+b0.5)×a,  0.2+2+a×b0.2a

valid attempt to express E(X) in one variable       M1

eg       0.2+4×0.5+a×(0.3a)+(0.2)×a,  2.2+0.1aa2,

           0.2+4×0.5+(0.3b)×b+(0.2)×(0.3b),   2.14+0.5bb2

correct value of greatest E(X)        (A1)

2.2025  (exact)

valid attempt to find least value        (M1)

eg       graph with minimum indicated, E(0)  and  E(0.3)

          (02.2)  and  (0.32.14) if E(X) in terms of a

          (02.14)  and  (0.32.2) if E(X) in terms of b

correct value of least E(X)        (A1)

eg       2.14  (exact)

difference =0.0625 (exact)       A1  N2

[6 marks]

b.

Examiners report

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

Syllabus sections

Topic 2—Functions » SL 2.4—Key features of graphs, intersections using technology
Show 100 related questions
Topic 4—Statistics and probability » SL 4.7—Discrete random variables
Topic 2—Functions
Topic 4—Statistics and probability

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