Question: 18. A point is taken at random from the interval (0, 1), all points being equally likely. A second point is then taken in the

18. A point is taken at random from the interval (0, 1), all points being equally likely.

A second point is then taken in the same way. Let X be the coordinate of the point halfway between these points. X is a continuous chance quantity with a probability density function having an inverted V graph as shown below:

1 x

0 2

(1/2, 2)

1 Write down the formula for f(x). Find the mean and variance of X. Find the formula for F(x) and graph F(x).

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