The probability density function, f(x), for any continuous random variable X, represents:
A)all possible values that X will assume within some interval a $\le$ x $\le$ b.
B)the probability that X takes on a specific value x.
C)the area under the curve at x.
D)the height of the function at x.

Question

The probability density function, f(x), for any continuous random variable X, represents:
A)all possible values that X will assume within some interval a $\le$  x $\le$  b.
B)the probability that X takes on a specific value x.
C)the area under the curve at x.
D)the height of the function at x.

Quizplus · Accepted Answer

The probability density function (pdf) for a continuous random variable X represents the relative likelihood of X taking values in a given interval, rather than the probability that X takes on a specific value. Therefore, choice A is incorrect. The area under the curve of the pdf represents the probability of X taking values within a specific interval, not at a specific value of X, so choice C is also incorrect. The pdf represents the height of the function at a given value of X, so choice D is correct.

The Probability Density Function, F(x), for Any Continuous Random Variable ≤\le≤

The Probability Density Function, F(x), for Any Continuous Random Variable $\le$