Let y 1 , y 2 , ... , y n be a random sample of size n from the pdf f Y ( y ; θ ) = 2 y θ 2 , 0 ≤ y ≤ θ . Find a formula for the method of moments estimate for θ . Compare the values of the method of moments estimate and the maximum likelihood estimate if a random sample of size 5 consists of the numbers 17, 92, 46, 39, and 56 (recall Question 5.2.12).
Let y 1 , y 2 , ... , y n be a random sample of size n from the pdf f Y ( y ; θ ) = 2 y θ 2 , 0 ≤ y ≤ θ . Find a formula for the method of moments estimate for θ . Compare the values of the method of moments estimate and the maximum likelihood estimate if a random sample of size 5 consists of the numbers 17, 92, 46, 39, and 56 (recall Question 5.2.12).
Solution Summary: The author calculates the formula for the method of moments estimate for theta and the maximum likelihood estimate if a random of size 5 consists of the number 17, 92, 46, 39, and 56.
Let
y
1
,
y
2
,
...
,
y
n
be a random sample of size n from the pdf
f
Y
(
y
;
θ
)
=
2
y
θ
2
,
0
≤
y
≤
θ
. Find a formula for the method of moments estimate for
θ
. Compare the values of the method of moments estimate and the maximum likelihood estimate if a random sample of size 5 consists of the numbers 17, 92, 46, 39, and 56 (recall Question 5.2.12).
Definition Definition Probability of occurrence of a continuous random variable within a specified range. When the value of a random variable, Y, is evaluated at a point Y=y, then the probability distribution function gives the probability that Y will take a value less than or equal to y. The probability distribution function formula for random Variable Y following the normal distribution is: F(y) = P (Y ≤ y) The value of probability distribution function for random variable lies between 0 and 1.
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