The density curve for a continuous random variable X has which of the following properties? a) Area under the curve equals 1 b) It can have negative values c) It represents discrete data points d) It is represented by a step function
The correct answer is (a) Area under the curve equals 1.
The density curve of a continuous random variable X represents the probability density function (pdf) of X. The area under the curve of the pdf represents the total probability of all possible values that X can take, which is equal to 1.
The density curve of a continuous random variable X has the following properties:
* The area under the curve between any two points on the x-axis represents the probability that X takes a value between those points. * The area under the curve from negative infinity to positive infinity is equal to 1. * The curve can never have negative values, as the probability of a continuous random variable taking on a negative value is zero. * The curve does not represent discrete data points, as a continuous random variable can take on any value within its domain, not just discrete points. * The curve is not represented by a step function, as it is a continuous function that can take on any value within its domain.
Therefore, the correct answer is (a) Area under the curve equals 1.
