# Range of the bounded expectation

I have a probability function $$P$$ depends on a standard normal random variable $$\eta$$. Given a random draw of $$\eta^r$$ from the standard normal distribution ($$\eta\~N(0,1)$$), I can get a probability $$P(\eta^r)$$. I want to know if the following formula has its range, or could be calculated directly. $$E(\sum_r\frac{1}{R}P(\eta^r)(1-P(\eta^r))\eta^r)$$. I know that there is a bound for the probability $$0=, and would this boundary of the multiplication of the probability help? $$P=\frac{e^{A_j+B_j\eta}}{\sum_je^{A_j+B_j\eta}}\ ,B_i>0 \ \forall i$$

Thanks a lot!