(c) A certain form of 'triangular' distribution has c.d.f. F(r) = 1- (1– 2)², 0

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(c) A certain form of 'triangular' distribution has c.d.f.
F(r) = 1– (1– 2)², 0<x <1,
which is plotted in Figure 1. (It is called a triangular distribution
because its p.d.f. is a line which, together with the axes, forms a
triangle.)
1
Figure 1 The c.d.f. F(x)
(i) Calculate the value of the upper quartile for this distribution.
[3]
(ii) On a copy of, or very rough sketch based on, Figure 1, show the
values of a and its corresponding quantile qa for the upper quartile
that you calculated in part (c)(i).
[2]
(x)-
Transcribed Image Text:(c) A certain form of 'triangular' distribution has c.d.f. F(r) = 1– (1– 2)², 0<x <1, which is plotted in Figure 1. (It is called a triangular distribution because its p.d.f. is a line which, together with the axes, forms a triangle.) 1 Figure 1 The c.d.f. F(x) (i) Calculate the value of the upper quartile for this distribution. [3] (ii) On a copy of, or very rough sketch based on, Figure 1, show the values of a and its corresponding quantile qa for the upper quartile that you calculated in part (c)(i). [2] (x)-
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