My Math Forum Expected Value

 March 11th, 2012, 06:31 PM #1 Newbie   Joined: May 2010 Posts: 12 Thanks: 0 Expected Value How can I calculate the expected value of $E[\displaystyle\frac{\overline{Y}}{1-\overline{Y}}]$ with $E[\overline{Y}]=\vartheta$? Thanks
 March 12th, 2012, 02:38 PM #2 Global Moderator   Joined: May 2007 Posts: 6,787 Thanks: 708 Re: Expected Value You can't. You need to know the distribution function for Y.
 March 17th, 2012, 09:27 PM #3 Newbie   Joined: May 2010 Posts: 12 Thanks: 0 Re: Expected Value sorry I forgot the distribution, the distribution is $y\sim{Bernoulli(\vartheta)} with 0<\vartheta<1$ Thanks
 March 18th, 2012, 01:09 PM #4 Global Moderator   Joined: May 2007 Posts: 6,787 Thanks: 708 Re: Expected Value Unless we are at cross purposes (I am not quite sure what the random variable is - you use y and Y[with overhead bar]), you can't get an expectation, since y has a non-zero probability of = 1.
 March 18th, 2012, 05:08 PM #5 Newbie   Joined: May 2010 Posts: 12 Thanks: 0 Re: Expected Value Y denote a Bernoulli$(\vartheta)$ random variable with $0<\vartheta<1$. I want estimate the odds ratio $\gamma=\displaystyle\frac{\vartheta}{1-\vartheta}$. I know that $\overline{Y}$ is a unbiased estimator of $\vartheta$. I want to show that $G=\displaystyle\frac{\overline{Y}}{1-\overline{Y}}$ is not a unbiased estimator of $\gamma$ and for that reason I want know $E[\displaystyle\frac{\overline{Y}}{1-\overline{Y}}]$
 March 19th, 2012, 02:29 PM #6 Global Moderator   Joined: May 2007 Posts: 6,787 Thanks: 708 Re: Expected Value Ybar being an unbiased estimator is (at least my understanding) is that you took a sample of a certain size and computed the mean. If my understanding is correct, then Ybar has a non-zero probability of = 1, so the estimate you are concerned about would be infinite.

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