Project

Probability Density Function

1. Transportation Planning:

A transportation planner determines that the average distance between cars on a certain highway is 200ft.

(a) Assuming that the distance between cars is exponentially distributed , determine the probability density function for the distance x between successive cars.

(b)
Graph the probability density function for and shade the region under the curve that represents the probability that the distance between two successive cars chosen at random is 40ft. or less.

(c) Integrate the probability density function from x = 0 to x = 50.

(d) What does the value of the integral represent?

2. Time to Failure:

The 'time to failure' t, in hours, of a certain machine is assumed to be exponentially distributed. Suppose the average time that will pass before a failure occurs is 100hr.

(a) Determine the probability density function for the 'time to failure' t.

(d)
Graph the probability density function for and shade the region under the curve that represents the probability that a failure will occur in 50 hr. or less.

(e) Integrate the probability density function from x = 0 to x = 75.

(d) What does the value of the integral represent?