Question

(a) which are properties of the t distribution?
it is bell - shaped.
it is symmetric about the mean.
the mean, median, and mode are equal to 0 and are located at the center of the distribution.
the curve approaches but never touches the x axis.
the standard deviation and variance are both 1.
the t distribution is actually a family of curves based on the concept of degrees of freedom, which is related to sample size.
as the sample size increases, the t distribution approaches the standard normal distribution.

Explanation:

• The \(t\) - distribution is bell - shaped, symmetric about the mean.
• The mean, median, and mode of the \(t\) - distribution are equal to \(0\) and located at the center of the distribution.
• The curve of the \(t\) - distribution approaches but never touches the \(x\) - axis.
• The \(t\) - distribution is a family of curves based on degrees of freedom (related to sample size).
• As the sample size increases, the \(t\) - distribution approaches the standard normal distribution.
• The standard deviation of the \(t\) - distribution is \(\sqrt{\frac{

u}{
u - 2}}\) for \(
u>2\) (where \(
u\) is the degrees of freedom), so it is not \(1\) in general.

Answer:

It is bell - shaped.
It is symmetric about the mean.
The mean, median, and mode are equal to \(0\) and are located at the center of the distribution.
The curve approaches but never touches the \(x\) axis.
The \(t\) distribution is actually a family of curves based on the concept of degrees of freedom, which is related to sample size.
As the sample size increases, the \(t\) distribution approaches the standard normal distribution.