Which of the following is not a characteristic of a probability density function f(x)?Multiple Choicef(x) becomes zero or approaches zero if x increases to +infinity or decreases to −infinity.f(x) is symmetric around the mean.The area under f(x) over all values of x equals one.f(x) ≥ 0 for all values of x.
Question
Which of the following is not a characteristic of a probability density function f(x)?Multiple Choicef(x) becomes zero or approaches zero if x increases to +infinity or decreases to −infinity.f(x) is symmetric around the mean.The area under f(x) over all values of x equals one.f(x) ≥ 0 for all values of x.
Solution
The statement "f(x) is symmetric around the mean" is not a characteristic of a probability density function f(x). While some probability density functions, like the normal distribution, are symmetric around the mean, this is not a requirement for all probability density functions.
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