A random variable $x$ is having probability distribution function is given by

$f(x)=\frac{e^{-k}{k}^x}{x!},x=0,1,2,3.....$

i$)$ Is it a valid distribution? Justify. If valid then find the following

ii$),P(x>2)$ with $k=2k=2$

iii$)$ P $(1$k$=2$