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## Main Question or Discussion Point

Let f(x;p) = p*f(x) + (1-p)*g(x) where f(x) is the pdf of r.v. X1 dist N(1,1) and g(x) is the pdf of r.v. X2 dist N(0,1). Find one-sided lower confidence limit for p based on a sample size n=1.

This question has been driving me crazy. Everything that I've tried seems to be going nowhere, am I missing something obvious. What's throwing me off is that the new pdf is a sum of two others, and its not entirely obvious what the distribution f(x;p) looks like.

Thanks

This question has been driving me crazy. Everything that I've tried seems to be going nowhere, am I missing something obvious. What's throwing me off is that the new pdf is a sum of two others, and its not entirely obvious what the distribution f(x;p) looks like.

Thanks