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10 marksContinuous Random Variables

CAPE Applied Mathematics Unit 2 · 2015 · Paper 2 · Question 4(a)(i)

A continuous random variable X has probability density function f(x) = a + bx for 0 < x < 1, and 0 otherwise. It is given that F(0.5) = 0.8.

Show that a = 2.2 and determine the value of b.

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  1. 4(a)(ii)Determine P(X > 0.5).[3 marks]
  2. 4(b)(i)Determine the value of m and n shown in the table.[3 marks]
  3. 4(b)(ii)Carry out a χ² goodness-of-fit test at the 5% significance level to determine whether the data may be modelled by a normal distribution with mean 9 and…[9 marks]

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