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Continuous random variables and the normal distribution — Question 310

Original QCE Vault practice · 4 marks

Q310 · Practice questionTechnology-freeComplex familiar4 marks

QUESTION 310 (4 marks)

A randomly selected origami session lasts XX hours with density f(x)=32x(2−x)f(x)=\dfrac32x(2-x) for 0≤x≤20\leq x\leq2, and zero otherwise.
Graph of the proposed expression 1.5x(2-x) on [0,2], with zeros at both ends and height 1.5 at x=1.
a)
Check whether this is a valid probability density.
[2 marks]
b)
If it is not valid, replace 32\dfrac32 by the correct constant.
[1 mark]
c)
Using the corrected density, determine P(X>1)P(X>1) without integration.
[1 mark]
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