Let X1,... , Xn Bernoulli(p), with n = 20 and p unknown. Let Y = X1+ ...+ X20. (a) What is the likelihood function of p conditional on the n = 20 Bernoulli observations? (b) What is the likelihood function of p conditional on y? (c) True or False, and briefly explain: Both likelihood functions result in the same MLE o

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2. Let X1, ..., Xn Bernoulli(p), with n = 20 and p unknown. Let Y = X1+ ...+ X20.
(a) What is the likelihood function of p conditional on the n = 20 Bernoulli observations? 4
(b) What is the likelihood function of p conditional on y?
(c) True or False, and briefly explain: Both likelihood functions result in the same MLE of p.
Answer this question without finding the MLE in each case.
(d) Consider the sample proportion of the Bernoulli variables, p=X. Show that Var(p) = p(1-p)/n.
Transcribed Image Text:2. Let X1, ..., Xn Bernoulli(p), with n = 20 and p unknown. Let Y = X1+ ...+ X20. (a) What is the likelihood function of p conditional on the n = 20 Bernoulli observations? 4 (b) What is the likelihood function of p conditional on y? (c) True or False, and briefly explain: Both likelihood functions result in the same MLE of p. Answer this question without finding the MLE in each case. (d) Consider the sample proportion of the Bernoulli variables, p=X. Show that Var(p) = p(1-p)/n.
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