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\centerline{Math 36 --- Daily Homework}

\centerline{Assigned: 9/20} 

\centerline{Due: 9/22}
  

\begin{questions}

\question 

\begin{enumerate}[label = (\alph*)]
\item Two events A and B are \textbf{independent} if the probability of A occuring does not depend on B (i.e. $P(A|B) = P(A|\neg B) = P(A)$) and vice versa. Prove that if A and B are independent, then 
$$P(A \cap B) = P(A)P(B).$$

\vspace{2 in}
\item Suppose you have a random variable X between 0 and 1 with the pdf 
$$f(x) = 2x.$$
Describe how X can be used to simulate a coin flip.

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