4. A random sample of size n is taken from a distribution with probability density function f(z) = :0 < ro0 where a is a parameter such that a > 0. (i) Show by evaluating the appropriate integral that, in the case a > 1, the mean of this distribution is given by Hint: when integrating, write z = (1+1) – 1 and exploit the fact that the integral of a density function is unity over its full range. (ii) Determine the method of moments estimator of a.
4. A random sample of size n is taken from a distribution with probability density function f(z) = :0 < ro0 where a is a parameter such that a > 0. (i) Show by evaluating the appropriate integral that, in the case a > 1, the mean of this distribution is given by Hint: when integrating, write z = (1+1) – 1 and exploit the fact that the integral of a density function is unity over its full range. (ii) Determine the method of moments estimator of a.
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 29CR
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Transcribed Image Text:4. A random sample of size n is taken from a distribution with probability density function
S(2) = :0 < roo
where a is a parameter such that a > 0.
(i) Show by evaluating the appropriate integral that, in the case a > 1, the mean of this
distribution is given by
Hint: when integrating, write r = (1+x) – 1 and exploit the fact that the integral of a density
function is unity over its full range.
(ii) Determine the method of moments estimator of a.
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