Originally Posted by

**carla1985** "The random variable X has a Poisson distribution with parameter λ = 3. By employing Markov’s inequality,

$\displaystyle P(|X|\geq\epsilon)\leq\frac{E(|X|k)}{\epsilon^k}$

calculate bounds for P (X ≥ 7) in the cases where k = 1, 2. Which of the two estimates is better?"

What I've done:

$\displaystyle Using\ P_X(k)=\frac{e^{-\lambda}\lambda^k}{k!}$

$\displaystyle with\ \lambda=3\ and\ k=1:\ P_X(k)=0.14936$

$\displaystyle with\ \lambda=3\ and\ k=2:$$\displaystyle \ P_X(k)=0.22404$

I'm not sure if thats right or have any idea which is a better estimate. Could someone help explain please? Thanks