The characteristics of the t distribution include:

The t distribution is indeed a family of similar probability distributions, which is one of its defining characteristics. Each member of the t distribution family is characterized by its degrees of freedom. As the number of degrees of freedom increases, the t distribution approaches the standard normal distribution. This family aspect makes the t distribution particularly useful in hypothesis testing and in constructing confidence intervals, especially when sample sizes are small and population standard deviations are unknown.

The mean of the t distribution is zero, which reflects its symmetry about the vertical axis at zero, but this is not what distinguishes it as a "family" of distributions. Additionally, while the t distribution has thicker tails compared to the normal distribution, it does not skew to the right; it is symmetric. The notion of approaching a uniform distribution is inaccurate, as the t distribution is not characterized by uniformity but rather varies based on the degrees of freedom.