diff --git a/theories/probability.v b/theories/probability.v index 55d7b0f1a..72ddd04ba 100644 --- a/theories/probability.v +++ b/theories/probability.v @@ -1509,6 +1509,8 @@ move=> iX. have := @dRV_expectation_comp _ _ T R R P (@measurable_set1 R) X. Admitted. +(* check that expecation_bernoulli is recoverable by bernoulli_pmf *) + Definition pmf (X : {RV P >-> R}) (r : R) : R := fine (P (X @^-1` [set r])). Lemma expectation_pmf (X : {dRV P >-> R}) : @@ -2992,7 +2994,7 @@ Qed. Lemma independent_mmt_gen_fun (X : {dRV P >-> bool}^nat) n t : let mmtX (i : nat) : {RV P >-> R} := expR \o t \o* (btr P (X i)) in independent_RVs P `I_n X -> independent_RVs P `I_n mmtX. -Admitted. +Admitted. (* from Reynald's PR, independent_RVs2_comp, "when applying a function, the sigma algebra only gets smaller" *) Lemma expectation_prod_independent_RVs (X : {RV P >-> R}^nat) n : independent_RVs P `I_n X ->