Chapter 5.2, Problem 1Q

A random sample of size $8–x_1=1,x_2=0,x_3=1,x_4=1,x_5=0,x_6=1,x_7=1$, and $x_8=0$–is taken from the probability function

$p_X\left(k;\theta \right)={\theta }^k{\left(1-\theta \right)}^{1-k},k=0,1;0<\theta <1$

Find the maximum likelihood estimate for $\theta$.