Statistical Inference — expectation of a mixture distribution

Let $x_1=\frac{17}{3},x_2=\frac{10}{3},x_3=\frac{13}{3},x_4=4$ be the observed values of a random sample of size 4 from the distribution having pdf $f(x,\theta)=\frac{1}{3}\left[\frac{1}{2\theta}e^{-\frac{x}{2\theta}}+\frac{1}{\theta^2}e^{-\frac{x}{\theta^2}}+e^{-x}\right]$; $x>0,\theta>0$. What is $E(X)$ equal to?