Suppose I have two biased coins.
I want to estimate the joint probability of both being heads.
SO for coin A, I make n tosses, and have x heads.
for coin B I make m tosses, and have y heads.
For coin A, the best estimate for the probability of a head is
u = x/n
the se for that is
se = sqrt(u*(1-u)/n)
And the 95% confidence bounds are
p = u +/- 1.96 * se.
But how do I get the equivalent bounds for both coins being heads? My
colleague said it was something to do with gaussians, but I can't find
any references on the interweb. I'd like to do similar calculations for more than 3,4,...,n coins.