I have a sequence of random variables $Y_t$ with the same distribution. Is there a way to show that they are independent (i.e., are an iid sequence), if we know that:
$\forall i \in \{1,\ldots,n\}: E[Y_i \mid Y_1,\ldots,Y_{i-1}]=E[Y_i]$
?
Thanks for your answers.