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Competitive Stats
Q7Section I (Objective (Q1–Q80))7 of 79

Distribution Theory — distribution of a ratio of normal combinations

Let X1,X2,X3,…,X7X_1, X_2, X_3, …, X_7 be iid random variables, each having the N(0,1)N(0,1) distribution. What is the distribution of the following?

2(X5−X6+X7)(X1+X2+X3)2+3X42\frac{\sqrt{2}(X_5-X_6+X_7)}{\sqrt{(X_1+X_2+X_3)^2+3X_4^2}}

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