supuestos := 
        x ∈ Reals && 
          1 > ρ > 0 && (Subscript[σ, 1]) > 0 && (Subscript[σ, 2]) > 
            0;
"f(x,y)"
nfxy = ((((1 - (ρ^2)))^(-1/2))/(2 π (Subscript[σ, 1]) (Subscript[σ, 2]))) 
        Exp[((-1)/(2 (1 - (ρ^2)))) ((((((x - (Subscript[μ, 1]))/(Subscript[σ, 1]))))^2) - 
                2*ρ (((x - (Subscript[μ, 1]))/(Subscript[σ, 1]))) (((y - (Subscript[μ, 2]))/(Subscript[σ, 2]))) + (((((y - (Subscript[μ, 2]))/(Subscript[σ, 2]))))^2))]

"Marginal de X"
nfx = 
      Integrate[nfxy, {y, -Infinity, Infinity}, 
        Assumptions -> (supuestos)]

"Marginal de Y"
nfy = 
      Integrate[nfxy, {x, -Infinity, Infinity}, 
        Assumptions -> (supuestos)]

"E(X|Y=y)"
nexy = 
      Integrate[x* (nfxy/nfy), {x, -Infinity, Infinity}, 
        Assumptions -> (supuestos)]

"E(Y|X=x)"
neyx = 
      Integrate[y (nfxy/nfx), {y, -Infinity, Infinity}, 
        Assumptions -> (supuestos)]

neyyx = 
      Integrate[(y^2) (nfxy/nfx), {y, -Infinity, Infinity}, 
        Assumptions -> (supuestos)]

"Varianza"
variance = neyyx - (neyx^2);
Simplify[%]

nexxy = 
      Integrate[(x^2) (nfxy/nfy), {x, -Infinity, Infinity}, 
        Assumptions -> (supuestos)]

"Varianza"
var = nexxy - (nexy^2);
Simplify[%]