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Probability - cumulative distribution and bias watch

    • Thread Starter

    I have 2 questions that I'm stuck on.

    The cumulative distribution function for X is

    0, if x is less than or = 0
    x, if x is between 0 and 1
    1, if x is greater than or = 0

    Then find the cumulative distribution function of the random variable Y = -2lnX

    Find the probability density function of Y and identify the distribution.
    Also determine variance of Y.

    Suppose that X1, X2,... ,Xn is a random sample of size n, from a normal distribution N(0,theta).

    State whether the following are biased or unbiased, justify this.
    If they are biased, calculate the bias.

    theta hat = sigma(from i=1 to n) (((Xi)^2)/n)

    theta2 hat = n*[sigma(from i=1 to n) (Xi/n)^2 ]^2

    Thanks for any help!
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Updated: December 3, 2011

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