The probability density function f(x) of a random variable X that is normally distributed is completely determined once the:
A) mean and median of X are specified
B) median and mode of X are specified
C) mean and mode of X are specified
D) mean and standard deviation of X are specified
E) mode and standard deviation of X are specified

Question

Quizplus · Accepted Answer

The probability density function of a normally distributed random variable is determined by its mean and standard deviation. The mean specifies the center of the distribution, and the standard deviation influences the spread of the distribution. Therefore, the correct answer is D, where both the mean and standard deviation are specified. The other choices are incorrect because they do not fully determine the probability density function of a normally distributed random variable.

The Probability Density Function F(x) of a Random Variable X