Let X1,..., Xn be an iid random sample from the Binomial(k, p) distribution, where p is known but k is unknown. For example, this could happen in an experiment where we flip a coin that we know is fair and observe x; heads, but we do not know how many times the coin was flipped. Suppose we observe values x1,..., xn of our random sample. In this problem, you will show that there is a unique maximum likelihood estimator of k. (a) difficult here? What is the likelihood function, L(k)? Why is maximization by differentiation (b) of k. What is the value of the likelihood when k < max x;? Based on this, what can you We have to take a different approach to finding the maximum likelihood estimator i=1,...,n conclude about the range of values the maximum likelihood estimator can take?

Let X1,..., Xn be an iid random sample from the Binomial(k, p) distribution, where p is known but k is unknown. For example, this could happen in an experiment where we flip a coin that we know is fair and observe x; heads, but we do not know how many times the coin was flipped. Suppose we observe values x1,..., xn of our random sample. In this problem, you will show that there is a unique maximum likelihood estimator of k. (a) difficult here? What is the likelihood function, L(k)? Why is maximization by differentiation (b) of k. What is the value of the likelihood when k < max x;? Based on this, what can you We have to take a different approach to finding the maximum likelihood estimator i=1,...,n conclude about the range of values the maximum likelihood estimator can take?

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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