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 about zero and resembles the standard normal distribution, especially as degrees of freedom increase.
For a $t$-distribution with degrees of freedom $\nu>1$, the mean exists and is equal to 0.
This is because the $t$-distribution is centered at 0 and has a bell shape.
However, if $\nu \leq 1$, the mean is undefined.
In most statistical contexts where $\nu>1$, which is common in real-world applications, the mean is considered to be 0.
Thus, the correct answer is $0$.