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i.i.d. Consider Y₁,..., Yn Bern(p). Consider the following estimator: p = n Y with probability n-1 with probability/ n Show that p is consistent but not asymptotically unbiased. Hint: We can write p = ZỸ +(1-Z)n where Z~ Bern (¹) and Z is independent of Y. Law of Total Probability may also be helpful.

i.i.d. Consider Y₁,..., Yn Bern(p). Consider the following estimator: p = n Y with probability n-1 with probability/ n Show that p is consistent but not asymptotically unbiased. Hint: We can write p = ZỸ +(1-Z)n where Z~ Bern (¹) and Z is independent of Y. Law of Total Probability may also be helpful.

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.3: Binomial Probability
Problem 2E: If a binomial experiment has probability p success, then the probability of failure is...
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i.i.d. Consider Y₁,..., Yn Bern(p). Consider the following estimator: p= n { JY with probability n-1 with probability 1 n Show that p is consistent but not asymptotically unbiased. Hint: We can write p = ZY+(1-Z)n Bern (¹) and Z is independent of Y. Law of Total Probability may also be helpful. where Z ~
Transcribed Image Text:i.i.d. Consider Y₁,..., Yn Bern(p). Consider the following estimator: p= n { JY with probability n-1 with probability 1 n Show that p is consistent but not asymptotically unbiased. Hint: We can write p = ZY+(1-Z)n Bern (¹) and Z is independent of Y. Law of Total Probability may also be helpful. where Z ~
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