2. Consider the negative binomial distribution with parameters r,p and having pmf nb(x;r,p) = Ꮖ (* + r − ¹) p*(1 − p)² p'(1-p) x = 0, 1, 2, 3, … …. (a) Supposer 2, then show that T-1 p = X+r−1 is an unbiased estimator for p. (Hint: write out E(p), then cancel out x+r −1 inside the sum). (b) A reporter wishing to interview five individuals who support a certain candidate (for presidency?) begins asking people whether they support (S) or not support (F) the can- didate. If they observe the following sequence of responses SFFSfffffffffffSSS, esti- mate p the true proportion of people who support the candidate. How does the estimate change if the following sequence of responses were observed ssssfffffffffffffs. Does it matter to the estimate when the first four S's appear in the sequence of responses?
2. Consider the negative binomial distribution with parameters r,p and having pmf nb(x;r,p) = Ꮖ (* + r − ¹) p*(1 − p)² p'(1-p) x = 0, 1, 2, 3, … …. (a) Supposer 2, then show that T-1 p = X+r−1 is an unbiased estimator for p. (Hint: write out E(p), then cancel out x+r −1 inside the sum). (b) A reporter wishing to interview five individuals who support a certain candidate (for presidency?) begins asking people whether they support (S) or not support (F) the can- didate. If they observe the following sequence of responses SFFSfffffffffffSSS, esti- mate p the true proportion of people who support the candidate. How does the estimate change if the following sequence of responses were observed ssssfffffffffffffs. Does it matter to the estimate when the first four S's appear in the sequence of responses?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:2. Consider the negative binomial distribution with parameters r,p and having pmf
nb(x;r,p) =
Ꮖ
(* + r − ¹) p*(1 − p)²
p'(1-p) x = 0, 1, 2, 3, … ….
(a) Supposer 2, then show that
T-1
p =
X+r−1
is an unbiased estimator for p. (Hint: write out E(p), then cancel out x+r −1 inside
the sum).
(b) A reporter wishing to interview five individuals who support a certain candidate (for
presidency?) begins asking people whether they support (S) or not support (F) the can-
didate.
If they observe the following sequence of responses SFFSfffffffffffSSS, esti-
mate p the true proportion of people who support the candidate.
How does the estimate change if the following sequence of responses were observed
ssssfffffffffffffs.
Does it matter to the estimate when the first four S's appear in the sequence of responses?
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