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Competitive Stats
Q28Section I (Objective (Q1–Q80))28 of 80

Distribution Theory — constant for a t-distributed ratio

Suppose that the five random variables X1,X2,…,X5X_1,X_2,…,X_5 are independent and each has a standard normal distribution. A constant C such that the random variable C(X1+X2)(X32+X42+X52)1/2\dfrac{C(X_1+X_2)}{(X_3^2+X_4^2+X_5^2)^{1/2}} will have a t-distribution, has value:

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