How to calculate these Expected Value

3 random variable X, Y, Z
ln(X) ~ Normal (0, Var(X))
ln(Y) ~ Normal (0, Var(Y))
ln(Z) ~ Normal (0, Var(Z))

X, Y, Z are not independently distributed but Covariance Matrix is
given

How to find
1. Prob(min(X,Y,Z)<k)
2. E(average(X,Y,Z))
3. E(average(X,Y,Z))|min(X,Y,Z)<k)
4. E(average(X,Y,Z))|min(X,Y,Z)>=k)

Are there any analytical solution? or I have to do simulation.

Thanks

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