Suppose the distribution of X for subjects having Y=1 is normal , and suppose the distribution of X for subjects having Y=0 is normal . Then why is a logistic regression curve? And why ?
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Note that Y is Bernoulli with probability (say) and we are given that . Just calculate and see what you get. I haven't done it all the way through, but it looks to me like you will get a function whose inverse is the logit.
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