We define a random process by the repeated coin toss experiment

$x(t)=\{\begin{array}{ccc}cost,& \text{h}\text{e}\text{a}\text{d}\text{f}\text{a}\text{c}\text{e}& up\\ 2t,& \text{t}\text{a}\text{i}\text{l}\text{f}\text{a}\text{c}\text{e}& up\end{array}$

Suppose that the probability of head and tail are equal.

a$.$ Determine the distribution function $F_x(x,\frac{1}{2}),F_x(x,1)$

b$.$ Determine the joint distribution function $F_x(x_1,x_2$;$\frac{1}{2},1)$