Question

The mean of $t$-distribution is

• A. $0$
• B. $1$
• C. $2$
• D. not defined

Hint:

The mean of $t$-distribution is $0$ if degrees of freedom $> 1$. Always check the condition on $\nu$ when dealing with moments.

Answer 1

The Correct Option is A

The \(t\)-distribution is symmetric around zero and approximates the standard normal distribution as the degrees of freedom increase.

For a \(t\)-distribution with degrees of freedom \(u > 1\), the mean is defined and equals 0.

This is due to the \(t\)-distribution being centered at 0 and having a bell-shaped curve.

However, when \(u \leq 1\), the mean is undefined.

In typical statistical applications where \(u > 1\) (frequent in practice), the mean is taken as 0.

Therefore, the correct answer is \(0\).