Suppose that I have a random sample $X_1, … ,X_n$ from a $N(0,\sigma^2)$ distribution. What is the distribution of $$\frac{\bar{X}}{S}$$ and what is it's standard deviation? Here $\bar{X}$ is the sample mean and $S$ is the sample standard deviation.
2026-03-29 15:59:35.1774799975
Sampling distribution of $\frac{\bar{X}}{S}$
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According to the Wiki article (see Combination of two or more independent random variables), $\sqrt{n}\dfrac{\bar{X}}{S}$ is the Student's $t$-distribution with $n − 1$ degrees of freedom.