T Distribution Theorem

Theorem

([@Ost20], Theorem 7.5.1) Let $Z \sim \mathcal{N}(0,1)$$ be [[Normal Distribution|standard normal random variable]], let$ V \sim \chi^2(n) $b e a [[C hi - Sq u a re d D i s t r ib u t i o n ∣ c hi - s q u a re d i s t r ib u t i o n]] w i t h$ n $d e g reeso ff ree d o m, an d a ss u m e t ha t$ Z $an d$ V$ are independence. Then the random variable $T = \frac{Z}{V / n}$ is a t random variable with n degrees of freedom.

References

D. Ostwald - The general linear model 20_21

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T Distribution Theorem

T Distribution Theorem

Theorem

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