Im trying to implement the EM algorithm on mixture model: $pg(x) + (1-p)h(x)$ where the sample $\bar{x} = (x_1, \ldots, x_n)$, is independently generated from the mixture, and $g(x) = e^{-x}$ and $h(x) = x^3 \frac{e^{-x}}{6}$. I want to calculate the E-step for this algorithm.
I already know that:
$$L(p | \bar{x}, \bar{Z}) = \prod_{i=1}^n pe^{-x_i} \mathbb{I}_{Z_i = 1} + (1 - p) x_i^3 \frac{e^{-x_i}}{6} \mathbb{I}_{Z_i = 0}$$.
I know that the E-step consists on calculating the expectation of the function $L$, but I don't know how to obtain this expected value. How do calculate the expected value on a mixture model? What should I do with the indicative function?
Any hints or advices are more than welcome.
