# Random sample from a population.

• Apr 30th 2010, 02:51 PM
gklove56
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?
• Apr 30th 2010, 07:14 PM
rubic
(a) State the distribution of the random variable X. Hence write down the expectation and variance of X.

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

(b) Let Y = NX/n. Show that Y is an unbiased estimator of m.
what is Y?
since it is random sampling we expect sample to have same characteristics as population
\$\displaystyle (X/n)=m/N\$
• May 1st 2010, 04:58 AM
gklove56
Quote:

Originally Posted by rubic
(a) State the distribution of the random variable X. Hence write down the expectation and variance of X.

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

(b) Let Y = NX/n. Show that Y is an unbiased estimator of m.
what is Y?
since it is random sampling we expect sample to have same characteristics as population
\$\displaystyle (X/n)=m/N\$

Thank you very much, you are great great!!!(Clapping)(Clapping)