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Consider discrete random variables $X$ and $Y$ with probabilities as follows:
$$ \begin{array}{l} P(X=0 \text { and } Y=0)=\frac{1}{4} \\ P(X=1 \text { and } Y=0)=\frac{1}{8} \\ P(X=0 \text { and } Y=1)=\frac{1}{2} \\ P(X=1 \text { and } Y=1)=\frac{1}{8} \end{array}$$

Given $X=1$, the expected value of $Y$ is

  1. $\frac{1}{4}$
  2. $\frac{1}{2}$
  3. $\frac{1}{8}$
  4. $\frac{1}{3}$

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