consider the probability mass function

$\displaystyle p_{X} (x; \theta) = \theta ^{x} (1 - \theta )^{1-x}, x = 0,1$

and suppose we observe a sample of 5 outcomes: 0, 0, 1, 0, 1.

(a) show howmaximum likelihood estimationcan be used to estimate the parameter $\displaystyle \theta$

(b) show how themethod of momentscan be used to estimate the parameter $\displaystyle \theta$