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2. Suppose ẞ is small enough, such that the result of Part (b) is applicable. Is this probability distribution a member of Exponential family? Let X., Xw be a sample of size from pxw. Find a complete sufficient statistics for a. Solution: Question 4. If we wish to study the distribution of X, the number of albino children (or children with a rare anomaly) in families with proneness to produce such children, a convenient sampling method is first to discover an albino child and through it obtain the albino count Xw of the family to which it belongs. If the probability of detecting an albino is ẞ, then the probability that a family with k albinos gets recorded is w(k) = 1 − (1 − ẞ)k, assuming the usual independence of Bernoulli trials. In such a case Pxw (k) = P(X = k) = w(k)P(X = k) E[w(X)] " k = 0, 1, 2, ... 1. Suppose X has the Pascal Distribution, that is P(X = k) = ak (1 + α)k+1' k = 0, 1, 2,... Find E(X) and show that w(k) k lim B→0 E[w(X)] E(X) State clearly the assumptions you need to establish this result. Solution:

2. Suppose ẞ is small enough, such that the result of Part (b) is applicable. Is this probability distribution a member of Exponential family? Let X., Xw be a sample of size from pxw. Find a complete sufficient statistics for a. Solution: Question 4. If we wish to study the distribution of X, the number of albino children (or children with a rare anomaly) in families with proneness to produce such children, a convenient sampling method is first to discover an albino child and through it obtain the albino count Xw of the family to which it belongs. If the probability of detecting an albino is ẞ, then the probability that a family with k albinos gets recorded is w(k) = 1 − (1 − ẞ)k, assuming the usual independence of Bernoulli trials. In such a case Pxw (k) = P(X = k) = w(k)P(X = k) E[w(X)] " k = 0, 1, 2, ... 1. Suppose X has the Pascal Distribution, that is P(X = k) = ak (1 + α)k+1' k = 0, 1, 2,... Find E(X) and show that w(k) k lim B→0 E[w(X)] E(X) State clearly the assumptions you need to establish this result. Solution:

MATLAB: An Introduction with Applications
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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2. Suppose ẞ is small enough, such that the result of Part (b) is applicable. Is this probability distribution a member of Exponential family? Let X., Xw be a sample of size from pxw. Find a complete sufficient statistics for a. Solution:
Transcribed Image Text:2. Suppose ẞ is small enough, such that the result of Part (b) is applicable. Is this probability distribution a member of Exponential family? Let X., Xw be a sample of size from pxw. Find a complete sufficient statistics for a. Solution:
Question 4. If we wish to study the distribution of X, the number of albino children (or children with a rare anomaly) in families with proneness to produce such children, a convenient sampling method is first to discover an albino child and through it obtain the albino count Xw of the family to which it belongs. If the probability of detecting an albino is ẞ, then the probability that a family with k albinos gets recorded is w(k) = 1 − (1 − ẞ)k, assuming the usual independence of Bernoulli trials. In such a case Pxw (k) = P(X = k) = w(k)P(X = k) E[w(X)] " k = 0, 1, 2, ... 1. Suppose X has the Pascal Distribution, that is P(X = k) = ak (1 + α)k+1' k = 0, 1, 2,... Find E(X) and show that w(k) k lim B→0 E[w(X)] E(X) State clearly the assumptions you need to establish this result. Solution:
Transcribed Image Text:Question 4. If we wish to study the distribution of X, the number of albino children (or children with a rare anomaly) in families with proneness to produce such children, a convenient sampling method is first to discover an albino child and through it obtain the albino count Xw of the family to which it belongs. If the probability of detecting an albino is ẞ, then the probability that a family with k albinos gets recorded is w(k) = 1 − (1 − ẞ)k, assuming the usual independence of Bernoulli trials. In such a case Pxw (k) = P(X = k) = w(k)P(X = k) E[w(X)] " k = 0, 1, 2, ... 1. Suppose X has the Pascal Distribution, that is P(X = k) = ak (1 + α)k+1' k = 0, 1, 2,... Find E(X) and show that w(k) k lim B→0 E[w(X)] E(X) State clearly the assumptions you need to establish this result. Solution:
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