Consider a distribution with probability mass function 

\(\rm f(x| θ)=\left\{\begin{matrix}\frac{1-θ}{2}, &if\ x = 0\\\ \frac{1}{2}&if\ x=1\\\ \frac{θ}{2}&if\ x=2\\\ 0&otherwise\end{matrix}\right.\)

where θ ∈ (0, 1) is an unknown parameter. In a random sample of size 100 from the above distribution, the observed counts of 0,1 and 2 are 20, 30 and 50 respectively. Then, the maximum likelihood estimate of θ based on the observed data is