Let X, Y be two Bernoulli random variables and denote by p = P[X = 1], q = P[Y = 1] and r = P[X = 1, Y = 1]. Let (X1, Y1), . . . , (Xn, Yn) be a sample of n i.i.d. copies of (X, Y ). Based on this sample, X and Y are independent, and r = pq. a)Define a=(summation (i=1 to n) (X i))/n and b=(summation (i=1 to n ) (X i))/n, c =((summation (i=1 to n)) (XiYi))/n. Prove that a,b,c respectively, are consistent estimators of p, q and r

Let X, Y be two Bernoulli random variables and denote by p = P[X = 1], q = P[Y = 1] and r = P[X = 1, Y = 1]. Let (X1, Y1), . . . , (Xn, Yn) be a sample of n i.i.d. copies of (X, Y ). Based on this sample, X and Y are independent, and r = pq. a)Define a=(summation (i=1 to n) (X i))/n and b=(summation (i=1 to n ) (X i))/n, c =((summation (i=1 to n)) (XiYi))/n. Prove that a,b,c respectively, are consistent estimators of p, q and r

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 31E

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