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What is the Likelihood function of a linear probability model?

I know the likelihood function is the joint probability density, but how to construct the likelihood function when we only have the probability $P(Y_i=1|X_i)$ and $P(Y_i=0|X_i)$?

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If the likelihood is the joint density of $X_i$ and $Y_i$, then you need to know $P(X_i)$ in order to get the joint density. Whether $P(X_i)$ is meaningful or not is something you need to consider. – Dilip Sarwate Dec 14 '11 at 12:43
What is a linear probability model? – Xi'an Dec 14 '11 at 14:21
The linear probability model is just linear regression with a binary outcome variable. – Charlie Dec 14 '11 at 15:48

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