The probability density function, f(x), for any continuous random variable X, represents:
A) all possible values that $X$ will assume within some interval $a \leq x \leq b$.
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 $a \leq x \leq b$.
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 represents the relative likelihood of different values of the continuous random variable, but it does not give the probability that the random variable takes on a specific value. The area under the curve of the probability density function (PDF) within some interval represents the probability of X taking a value within that interval. The height of the function at a particular value of X gives some idea of the relative likelihood of X taking that value, but it does not represent a probability. Therefore, D is the best option as it represents the height of the function at a specific value of X.

The Probability Density Function, F(x), for Any Continuous Random Variable XXX

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