Question: Prove that the following algorithm is equivalent to the Accept-Reject algorithm: 1. Generate X g; 2. Generate U | X = x U[0,Mg(x)]; 3. Accept

Prove that the following algorithm is equivalent to the Accept-Reject algorithm:

1. Generate X g;

2. Generate U | X = x U[0,Mg(x)];

3. Accept Y = X if U f(x);

4. Return to 1. otherwise

This is equivalent to prove that P(Y < y) = P(X < x | U < f(x)).

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