(a) What is the method of moments estimate of 0?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 20E
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3. Suppose that X is a discrete random variable with the following probability mass
function where 0 <0 <1 is a parameter:
X
1
P(X)
20/3 0/3
2(1 – 0)/3
(1 – 0)/3
The following 10 independent observations were taken from such a distribution:
(3,0, 2,1, 3, 2, 1,0, 2, 1).
(a) What is the method of moments estimate of 0?
The theoretical mean is:
3
E(X)Σap ().
r=0
20
+1x
3
2(1 – 0)
+ 3 x
3
(1 – 0)
= 0 x
+ 2 x
3
= 7/3 – 20
%3D
Transcribed Image Text:3. Suppose that X is a discrete random variable with the following probability mass function where 0 <0 <1 is a parameter: X 1 P(X) 20/3 0/3 2(1 – 0)/3 (1 – 0)/3 The following 10 independent observations were taken from such a distribution: (3,0, 2,1, 3, 2, 1,0, 2, 1). (a) What is the method of moments estimate of 0? The theoretical mean is: 3 E(X)Σap (). r=0 20 +1x 3 2(1 – 0) + 3 x 3 (1 – 0) = 0 x + 2 x 3 = 7/3 – 20 %3D
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