Which of the following is a property of the $S\text{'}t$-distribution?

• A. It is defined only for positive values.
• B. Its mean is always greater than $0$.
• C. It has heavier tails than the standard normal distribution.
• D. It is symmetric about $0$.

Answer: (D)

Verified step by step guidance

1. Recall the definition of the Student's t-distribution: it is a probability distribution that arises when estimating the mean of a normally distributed population in situations where the sample size is small and population standard deviation is unknown.
2. Understand the shape and properties of the t-distribution: it is symmetric about zero, similar to the standard normal distribution, but with heavier tails.
3. Recognize that 'heavier tails' means the t-distribution has more probability in the tails compared to the normal distribution, which accounts for greater variability in small samples.
4. Note that the t-distribution is defined for all real numbers, not just positive values, so it is not limited to positive values only.
5. Remember that the mean of the t-distribution is zero (when degrees of freedom are greater than 1), so it is not always greater than zero.