Markov Inequality $Pr(yn¡Ý¦Å)¡ÜE[=?iso-8859-1?Q?$Pr(yn¡Ý¦Å)=A1=DCE[yn]/g?==?iso-8859-1?Q?$Pr(yn¡Ý¦Å)¡ÜE[yn]/g(=A6=C5?=)$

Markov Inequality $Pr(yn¡Ý¦Å)¡ÜE[yn]/g(¦Å)$

I am trying to proof this markov inequality form:
For $y_n$ is a a nonnegative random variable and $\varepsilon>0$, and
$E[y_n]>0$, then
$Pr(y_n \geq\varepsilon)\leq E[y_n]/g(\varepsilon)$
Can I show this proof by using
$E[y_n]=Pr(y_n \geq\varepsilon)E[y_n|y_n\geq g(\varepsilon)]$$+Pr(y_n
<\varepsilon)E[y_n|y_n< g(\varepsilon)]$