The density curve for a continuous random variable X has which of the following properties?
A)The probability of any event is the area under the density curve and above the values of X that make up the event.
B)The total area under the density curve for X must be exactly 1.
C)The probability of any event of the form X = constant is 0.
D)All of the answer options are correct.

Question

Quizplus · Accepted Answer

A) This is true for all continuous random variables as they do not have discrete points of probability.
B) This is also true for all probability density functions as they represent the total probability of all possible events.
C) This is true because the probability of any single point in a continuous distribution is zero, only intervals have positive probability.
Therefore, all options are correct.

The Density Curve for a Continuous Random Variable X Has