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Math Help - Random sample from a population.

  1. #1
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    Random sample from a population.

    please please help me out for these question below. They are very important to me. As I am not good on Statistic and I don't have the model answers for them, I really want someone who can show me the answers about them. Therefore, I can check if i was doing the questions in the right way.

    Thank you very much!!!

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    Question 5---In a large population of N adults, let m be the number who are obese. The number N is known, but the number m is not known. A random sample of n people is chosen, where n is much smaller than N. Let X be the number of obese people in the sample.

    (a) State the distribution of the random variable X. Hence write down the expectation and variance of X.
    (b) Let Y = NX/n. Show that Y is an unbiased estimator of m.
    (c) Find the standard deviation of Y .
    (d) Suppose that N = 2, 000, 000 and n = 1, 000. To what accuracy should the estimate of m be reported?
    Last edited by mr fantastic; April 30th 2010 at 04:03 PM. Reason: Re-titled.
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  2. #2
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    (a) State the distribution of the random variable X. Hence write down the expectation and variance of X.

    it is Binomial dist(n, m/N)
    Expectation = (nm)/N
    Variance = ((nm)(N-m))/N^2

    (b) Let Y = NX/n. Show that Y is an unbiased estimator of m.
    i am not sure about this part of the question,
    what is Y?
    since it is random sampling we expect sample to have same characteristics as population
    (X/n)=m/N
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  3. #3
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    Quote Originally Posted by rubic View Post
    (a) State the distribution of the random variable X. Hence write down the expectation and variance of X.

    it is Binomial dist(n, m/N)
    Expectation = (nm)/N
    Variance = ((nm)(N-m))/N^2

    (b) Let Y = NX/n. Show that Y is an unbiased estimator of m.
    i am not sure about this part of the question,
    what is Y?
    since it is random sampling we expect sample to have same characteristics as population
    (X/n)=m/N
    Thank you very much, you are great great!!!
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