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Determining the density of the estimate of the proportion

  1. Feb 22, 2013 #1
    1. The problem statement, all variables and given/known data

    In a binomial experiment with number of trials n=1, the probability of success p represents a proportion. The ratio of successes X to the n can be used as an estimator of the proportion. For large n the number of successes in a binomial experiment is normally distributed, so that:
    z=(X-np)/√(npq)
    has zero mean and unit variance. Use the above information to determine the density for the estimate of the proportion ρ=X/n.

    2. Relevant equations

    Density function for normal distribution: f(x)=1/(σ√(2∏))*e^-((x-μ)^2/(2σ^2)) where μ=mean and σ=standard deviation

    When constructing a random variable z with zero mean and unit variance:
    z=(X-μ)/σ

    3. The attempt at a solution

    Can I simply plug in μ=np and σ=√(npq) into my equation for a normal distribution? μ and σ are for the sample space, do I need to change tactics for the estimate of the proportion? Thanks, any help/guidance is appreciated.
     
  2. jcsd
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