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
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section: Chapter Questions
Problem 8CR
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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
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