$\displaystyle p=(X=k)=\left\{\begin{array}{cc}p(1-p)^{k-1}&\mbox{k=1,2,3...}

\\ 0 & \mbox{ elsewhere } \end{array}\right.

\\ \mbox{ where } 0<p<1 \\$

how do I show that

i)$\displaystyle M_x(t)=\frac{pe^t}{1-(1-p)e^t}$

ii)use the mgf to find the mean and variance of X and

iii) find P(X + Y = 2)?

I'm lost with mgf's, I've searched the web but just definitions are given so I'm hoping to find examples