# Confusion related to EM algorithm

I was reading this tutorial related to EM algorithm at http://aass.oru.se/~tdt/ml/extra-readings/EM_algorithm.pdf. As given in the tutorial

we can see that at each E step we calculate the expectation of the likelihood over the posterior distribution of the hidden variables and them maximize it.The expected log likelihood over the posterior distribution hidden variables is upper bounded by the likelihood over the observed data only.

My questions are:

• Why is $L(\theta)$ non convex? Isn't it possible for $L(\theta)$ to be convex?
• Further why is $l(\theta | \theta_n)$ a convex function as shown in the figure?