Let X∼Exp(1)X \sim \text{Exp}(1)X∼Exp(1) and Y∣X=x∼LogNorm(0,x)Y \mid X = x \sim \text{LogNorm}(0,x)Y∣X=x∼LogNorm(0,x). Find Cov(X,Y)(X,Y)(X,Y). Note that we say a random variable R∼LogNorm(μ,σ2)R \sim \text{LogNorm}(\mu,\sigma^2)R∼LogNorm(μ,σ2) if log(R)∼N(μ,σ2)\log(R) \sim N(\mu,\sigma^2)log(R)∼N(μ,σ2).
