Let X1, X2,.......Xn be a random sample of size n from a continuous distribution symmetric about...

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Let X_1, X_2,.......X_n be a random sample of size n from a continuous distribution symmetric about $\small \theta$ .

For testing H_0:= 10 vs H_1: $\small \theta$ < 10, consider the statistic T^- = $\tiny \sum_{i-1}^{n}$ Ri⁺(1- $\small \psi$ _i),

where $\small \psi$ _i =1 if X_i>10 , 0 otherwise; and R_i⁺ is the rank of (X_i - 10) among |X₁ -10|, |X₂-10|......|X_n -10|.

1. Find the null mean and variance of T^- .

2. Find the exact null distribution of T^- for n=5.

math Statistics-And-Probability

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Let X1, X2,.......Xn be a random sample of size n from a continuous distribution symmetric about...

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