Assume Normal distribution with known mean=a and known deviation=s. Now let's create slightly different distribution from this distribution: 1. we assume that all values of new distribution smaller than c become zero, and 2. all values bigger than d become d and 3. all values of the distribution between c and d will stay as normal distribution. What is the expected value of this new distribution.
Answer= [probability of x being less than c]x0+[probability of x being bigger than d]xd+[probability of x being in the interval of c and d]x[expected value].
I just can not calculate only [expected value] which is expected value of the interval. It should be definite integral, however, i am confused with coefficients in front of integral.