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

Quizplus · Accepted Answer

The probability density function f(x) of a normal distribution is completely determined by its mean and variance. The mean determines the location of the peak of the curve, while the variance determines the spread of the curve. The median and mode may be different from the mean for a normal distribution, but they do not determine the shape of the curve. Therefore, the correct answer is D, mean and variance of X are specified.

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