Question

Which of the following statements describes the probability density function of the normal variable X with mean Mu and variance Sigma square?

a) It is a symmetric distribution
b) It follows a uniform distribution
c) It is a discrete distribution
d) It is not related to the mean and variance

Answer 1

The probability density function of a normal variable is a symmetric distribution that is bell-shaped and defined by its mean and variance.

Step-by-step explanation:

The question pertains to the probability density function (PDF) of a normal variable X with mean μ and variance σ^2. A probability density function of a normal or Gaussian distribution has certain characteristics:

• It is a symmetric distribution around its mean.
• Each normal distribution is defined by its mean (μ) and variance (σ^2).
• The shape of the distribution is bell-shaped and continuous, not uniform or discrete.
• The mean, median, and mode of a normal distribution are all equal.
• The area under the curve of a PDF is equal to 1.

Therefore, the correct statement that describes the probability density function of the normal variable X is that it is a symmetric distribution.