how can we find joint probability mass function of discrete random variables X and Y, if we are given marginal distribution of X as well as the the conditional distributions of Y given X ? Thanks for the help.
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1$P(X = m , Y = n) = P(X = m) \times P(Y = n | X = m)$ should help. – Sarvesh Ravichandran Iyer Oct 30 '19 at 06:53
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Thank you for the help, it worked for me ! Is there a way i can mark it as a solution. – Malick Oct 30 '19 at 07:27
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You can mark what I've written below. If it feels like too little, then add a simple example to your question and I will work it out if you like. – Sarvesh Ravichandran Iyer Oct 30 '19 at 07:39
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We have :
$$ P(X = m, Y = n) = \underbrace{P(X = m)}_{\text{marginal}}\underbrace{P(Y = n | X = m)}_{\text{conditional}} $$
The marginal is given, the conditional is given, thus the joint is recovered. This step is often skipped even in elementary textbooks, so it is good you asked.
Sarvesh Ravichandran Iyer
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