If y has a binomial distribution with n trials and success probability p, show that Y/n is a consistent estimator of p. Can someone show how to show this. I appreciate it any and all help. thanks.
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Hello, Yn=X1+...+Xn, where the Xi's are independent Bernoulli distributions B(p). Law of large numbers : Yn/n converges to E[X1] almost surely, and hence in probability -> consistent.
Originally Posted by jzellt If y has a binomial distribution with n trials and success probability p, show that Y/n is a consistent estimator of p. Can someone show how to show this. I appreciate it any and all help. thanks. To show that Y/n is a consistent estimator of p, it is sufficient to show that and .
Originally Posted by Sambit To show that Y/n is a consistent estimator of p, it is sufficient to show that and . But here it may be much easier to prove convergence in probability, since we obviously have the law of large numbers ?
Originally Posted by Moo But here it may be much easier to prove convergence in probability, since we obviously have the law of large numbers ? Basically both the procedures need same labour which is very little indeed. Since , Obviously which gives and , so as . No tough job
there are a lot of meanings to consistency, strong, weak... I was curious as to what was meant here.
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