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[See Solution] Suppose X is a uniform random variable between 0 and 1 and Y \mid X follows a distribution with pdf shown below. f(y \mid x)=y/x \text for

Question: Suppose \(X\) is a uniform random variable between 0 and 1 and \(Y \mid X\) follows a distribution with pdf shown below.

\[f(y \mid x)=\frac{y}{x} \quad \text { for } 0

  1. (5pts) Find the conditional variance of \(Y \mid X\).
  2. (5pts) Determine the marginal distribution of \(Y\).

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