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Q25Section A (Section A)25 of 60

Expectation of a chi-square ratio

Let X1,X2,X3,X4,X5X_{1},X_{2},X_{3},X_{4},X_{5} be a random sample from N(0,1)N(0,1) distribution and let W=X12X22+X32+X42+X52W=\dfrac{X_{1}^{2}}{X_{2}^{2}+X_{3}^{2}+X_{4}^{2}+X_{5}^{2}}. Then E(W)E(W) equals

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