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 variance of X are specified.

Question

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 variance of  X  are specified.

Quizplus · Accepted Answer

The probability density function of a normally distributed random variable is determined by its mean and variance. The mean specifies the location of the center of the distribution, while the variance controls the spread or width of the distribution. The other options are not sufficient to determine the probability density function of a normal random variable. For example, a normal distribution can have multiple modes or no mode at all, and the median may not coincide with the mean in skewed distributions.

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