proposition: Lemma variance_cst r : 'V_P[cst r] = 0%E.
proof: Proof. rewrite /variance unlock expectation_cst/=. rewrite [X in 'E_P[X]](_ : _ = cst 0%R) ?expectation_cst//. by apply/funext => x; rewrite /GRing.exp/GRing.mul/= subrr mulr0. Qed.
imports: mathcomp(all_ssreflect) mathcomp(ssralg poly ssrnum ssrint interval finmap) mathcomp(mathcomp_extra boolp classical_sets functions) mathcomp(cardinality) HB(structures) exp numfun lebesgue_measure lebesgue_integral reals ereal signed topology normedtype sequences esum measure exp numfun lebesgue_measure lebesgue_integral