The random variable X has the cumulative distribution function F(x) whose value or derivative F(x) is shown below for various values of x.

F(0) 0.

F(x)

1 8

, for 0  x  2.

P{X 2}

1 2

, so F(2)

3 4

.

F(x)

1 4

, for 2  x  3.

F(3) 1.

Generate four random observations from this probability distribution by using the following uniform random numbers:

3 4

, 1 2

, 1 4

, 7 8

. Also calculate the sample average and compare it with the true mean

(

1 8

5

) for this probability distribution.