1) verify Property 2 of the definition of a probability density function over the given interval.

f(x)=41?x,[1,3]

2) Find k such that each function is a probability density function over the given interval. Then write the probability density function.

f(x)=kx2,[?1,1]

3) Refer to example 10. A transportation planner determines that the average distance between cars on a certain highway is 200 ft. What is the probability that the distance between two successive cars, chosen at random, is 10 ft or less?

I EXAMPLE 10 Business: Transportation Planning. The distance x, in feet, be- tween successive cars on a certain stretch of highway has a probability density function f(x) = ke'b', forO S x