I'm stuck on the following:
Consider a random variable $X$ whose probability mass function is given by: $ p(x)= \begin{cases} 0.1,\quad &x=-3\\ 0.2, &x=0\\ 0.3, &x=2.2\\ 0.1, &x=3\\ 0.3, &x=4\\ 0,&\text{otherwise} \end{cases} $ Let $F(x)$ be the corresponding cdf. Find $E(F(X))$.
Thanks.
Thanks for the edits, Stefan. This is not a homework problem. I'm studying for my P1 exam after being out of school for some time.
So far, I have: $ F(x)= \begin{cases} 0,\quad &x<-3\\ 0.1, &-3<=x<0\\ 0.3, &0<=x<2.2\\ 0.6, &2.2<=x<3\\ 0.7, &3<=x<4\\ 1,& 4<=x \end{cases} $