Reed Bartlett
05/21/2024 · Primary School

Theorem : If \( Z \sim N(0,1) \) and \( U-x^{2}(v) \) and in addition, \( Z \) and \( U \) are independent, then the random variable \( W \) defined by \( W=\frac{Z}{\sqrt{\frac{U}{V}}} \) has a \( t \)-distribution with \( v \) degrees of freedom.

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إذا كان \( Z \) يتبع التوزيع الطبيعي القياسي \( N(0,1) \) و \( U \) يتبع توزيع كاي تربيع \( \chi^{2}(v) \) و \( Z \) و \( U \) مستقلان، فإن المتغير \( W = \frac{Z}{\sqrt{\frac{U}{v}}} \) يتبع توزيع \( t \) بدرجات حرية \( v \).

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