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Q43Section C (Section C)43 of 60

Comparing two averages of independent normal variables

Let X1,X2,X3,X4,X5X_1,X_2,X_3,X_4,X_5 be independent random variables with X1∼N(200,8)X_1\sim N(200,8), X2∼N(104,8)X_2\sim N(104,8), X3∼N(108,15)X_3\sim N(108,15), X4∼N(120,15)X_4\sim N(120,15) and X5∼N(210,15)X_5\sim N(210,15). Let U=X1+X22U=\frac{X_1+X_2}2 and V=X3+X4+X53V=\frac{X_3+X_4+X_5}3. Then P(U>V)P(U>V) equals __________________

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