Let X be a continuous random variable whose probability density function is:

 for  0 < x < 1

What is ?

An oil company conducts a geological study that indicates that an exploratory oil well should have a 20% chance of striking oil. What is the probability that they have to drill seven wells until the third strike occurs?

A repair team is responsible for a stretch of oil pipeline 4 km long. The distance (in km) at which any fracture occurs, , can be represented by a uniformly distributed random variable, with probability density function f(x) = 0.25. The mean and the standard deviation of the distance  at which any fracture occurs are, respectively,

A continuous uniform distribution has the parameters a = 4 and b = 10. The F(20) is:

The lifetime of a certain type of light bulb is exponentially distributed with a mean of 1000 hours. If a household has 4 of these light bulbs, what is the probability that at least two of them burn out before 800 hours?

The amount of time (in minutes) a postal clerk spends with his or her customer is a random variable, , with the following density function , . The probability that this clerk spends four to six minutes with a randomly selected customer is,

Consider the figure below. It shows three cumulative distributions functions for the exponential distribution with various parameters:

Identify the color of these distributions.