We have N measurements collected as i.i.d. observations from a random variable x and the pdf of measurements is in binomial form as p(x[r] | s)=(»)s*In](1 – s)(N-x[n]) for n = 0,..(N-1). x[n], where s denotes the probability of success. a. Write p(x | s) and design a ML (Maximum Likelihood) estimator for s. b. Show that the ML estimator is unbiased. (Hint: E[x [n] ]= Ns for the binomial distribution) c. Calculate the CRLB (Cramer-Rao lower bound).
We have N measurements collected as i.i.d. observations from a random variable x and the pdf of measurements is in binomial form as p(x[r] | s)=(»)s*In](1 – s)(N-x[n]) for n = 0,..(N-1). x[n], where s denotes the probability of success. a. Write p(x | s) and design a ML (Maximum Likelihood) estimator for s. b. Show that the ML estimator is unbiased. (Hint: E[x [n] ]= Ns for the binomial distribution) c. Calculate the CRLB (Cramer-Rao lower bound).
MATLAB: An Introduction with Applications
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![We have N measurements collected as i.i.d. observations from a random variable x and the pdf of measurements is
in binomial form as
N
p(x[r] |s)=()
s*[n] (1-s)(N-*[n]) for n = 0,..(N-1).
1....
where s denotes the probability of success.
a. Write p(x | s) and design a ML (Maximum Likelihood) estimator for s.
b. Show that the ML estimator is unbiased. (Hint: E[ x [n] ]= Ns for the binomial distribution)
c. Calculate the CRLB (Cramer-Rao lower bound).
d. Show that the estimator is efficient.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6b07e939-b1a8-4782-988f-4eb8c4ec201f%2Fdd5a41cd-0395-4d57-8b66-cbe26b446c34%2Fiudmj3l_processed.jpeg&w=3840&q=75)
Transcribed Image Text:We have N measurements collected as i.i.d. observations from a random variable x and the pdf of measurements is
in binomial form as
N
p(x[r] |s)=()
s*[n] (1-s)(N-*[n]) for n = 0,..(N-1).
1....
where s denotes the probability of success.
a. Write p(x | s) and design a ML (Maximum Likelihood) estimator for s.
b. Show that the ML estimator is unbiased. (Hint: E[ x [n] ]= Ns for the binomial distribution)
c. Calculate the CRLB (Cramer-Rao lower bound).
d. Show that the estimator is efficient.
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