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# Probability - cumulative distribution and bias watch

1. I have 2 questions that I'm stuck on.

1)
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.

2)
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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