Which of the following must be specified in order to completely determine the probability density function f(x) of a random variable X that is normally distributed?
A) the mean and median of X
B) the median and mode of X
C) the mean and mode of X
D) the mean and standard deviation of X

Question

Quizplus · Accepted Answer

In order to completely determine the probability density function of a normal distribution, we need to know two parameters: the mean and the standard deviation. Choice A is incorrect because the normal distribution is not necessarily symmetric and therefore the mean and median may not be equal. Choice B is also incorrect for the same reason, and because the mode is not a useful parameter to determine the probability density function. Choice C is incorrect because, again, the mode is not a useful parameter in determining the probability density function.

Which of the Following Must Be Specified in Order to Completely