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Q55Section ST (Statistics (Q11–Q65))55 of 65

Bernoulli U-statistic statements

Let X1,X2,X3X_1,X_2,X_3 be a random sample of size 3 from a population having Bernoulli distribution with parameter pp, where p∈(0,1)p \in (0,1) is unknown. Define T1(Xi,Xj,Xk)=Xi−Xj(1−Xk)T_1(X_i, X_j, X_k) = X_i - X_j(1 - X_k), T2(Xi,Xj,Xk)=12(XiXj+XjXk)T_2(X_i, X_j, X_k) = \frac12 (X_iX_j + X_jX_k), for i,j,k=1,2,3;i≠j≠ki,j,k = 1,2,3; i \ne j \ne k. Let x1,x2,x3x_1,x_2,x_3 denote realizations from the random sample. Then which of the following statements is/are true?

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Options

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