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 {Xi, Yi}ni=1be a sample of n i.i.d. copies of (X, Y ). Based on this sample, we want to test whether X and Y are independent, i.e., whether r =pq

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Q: Let X, Y be two Bernoulli random variables and denote by p = P (X = 1),      q = P (Y = 1) and r = P…

A: 1] p=P(X=1) 2] q=P(Y=1) 3] r=P(X=1,Y=1)

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Q: Let X, Y be two Bernoulli random variables and denote by p = P (X = 1), q = P (Y = 1) and r = P (X =…

A: X~Bernoulli(p)Y~Bernoulli(q)fx=1-p, if x =0=p, if x=1f(y)=1-q, if y=0=q, if y=1 r=P(X=1,Y=1)

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.