(i) Calculate the value of the upper quartile for this distribution. (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).

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(c) A certain form of ‘triangular' distribution has c.d.f.
F(x) = 1 − (1 − x)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.)
F(x)
1
Figure 1
X
The c.d.f. F(x)
1
(i) Calculate the value of the upper quartile for this distribution.
(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).
Transcribed Image Text:(c) A certain form of ‘triangular' distribution has c.d.f. F(x) = 1 − (1 − x)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.) F(x) 1 Figure 1 X The c.d.f. F(x) 1 (i) Calculate the value of the upper quartile for this distribution. (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).
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