Let A and B be some continuous random variables. We proceed as follows: we take a coin with bias b and flip it. If heads, we inspect A, if tails we inspect B. Call this resulting random variable C/

Sandra Terrell

Sandra Terrell

Answered question

2022-08-10

Let A and B be some continuous random variables. We proceed as follows: we take a coin with bias b and flip it. If heads, we inspect A, if tails we inspect B. Call this resulting random variable C.
Now say I can observe C and want to figure out if the coin was heads or tails, i.e. I want to compute Pr [
One thought I had was to approximate the coin toss with a continuous random variable K with pdf:
k ( x ) = b ,  for  x [ 1 , 0 ]
k ( x ) = 1 b ,  for  x [ 0 , 1 ]
Then one could compute the joint density function for K and C and compute Pr [ K < 0 | C = c ] from there. But this looks clunky and ugly. Is there a better way?

Answer & Explanation

Abdiel Murillo

Abdiel Murillo

Beginner2022-08-11Added 8 answers

To expand slightly on the great answer, if p and q are probabilities of C being A and B respectively, then

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