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Competitive Stats
Q59Section I (Objective (Q1–Q80))59 of 80

Distribution Theory — constant making a t-distributed ratio

Suppose that the random variables X1X_1, X2X_2, X3X_3, X4X_4, X5X_5 are independent and each has a standard normal distribution. A constant CC such that the random variable C(X4+X5)(X12+X22+X32)1/2\dfrac{C(X_4+X_5)}{\left(X_1^2+X_2^2+X_3^2\right)^{1/2}} will have a t-distribution, has value:

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