Question

The following density function describes a random variable X.

f(x)=x/81 if 0 14 years ago

Answer 1

The graph of f consists of a line segment from (0,0) to (9, 1/9) and a line segment from (9, 1/9) to (18, 0)

A) Draw in vertical line segments at x = 1 and x = 8 that extend from the x-axis to the graph of f. The area under the graph of f, above the x-axis, and between these two vertical segments is the probability that x lies between 1 and 8. This region is a trapezoid with height (8-1) = 7 and bases of length (1/81) and (8/81). The area of a trapezoid is ½h(b1 + b2) so the probability is ½(7)(9/81) = 7/9. If you've had integral calculus, it is

8
∫ (x/81) dx
1

For (B), do the same process. You'll need to divide the region up into two trapezoids sharing a base at x = 9. Again, if you've had integral calculus the probability is given by

9................13
∫ (x/81) dx + ∫ [(18 - x)/81] dx
6..................9..

Answer 2

Thank you!!