Suppose that X is a discrete random variable with

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 31CR
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Suppose that X is a discrete random variable with
P(X = 0) :
P(X = 1)
%3D
P(X = 2)
(1 – )
||
P(X = 3) = (1– 0),
where 0 <0 < 1 is the parameter of interest. The following 10 independent observations were taken
from such a distribution: (3,0, 2, 1, 3, 2, 1, 0, 2, 1).
a)
Find the method of moments estimator and estimate of 0.
b)
Find an approximate standard error for your estimate.
c)
Find the maximum likelihood estimate of 0.
N 3112 2/3
Transcribed Image Text:Suppose that X is a discrete random variable with P(X = 0) : P(X = 1) %3D P(X = 2) (1 – ) || P(X = 3) = (1– 0), where 0 <0 < 1 is the parameter of interest. The following 10 independent observations were taken from such a distribution: (3,0, 2, 1, 3, 2, 1, 0, 2, 1). a) Find the method of moments estimator and estimate of 0. b) Find an approximate standard error for your estimate. c) Find the maximum likelihood estimate of 0. N 3112 2/3
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