For $\lambda > \mu$, consider independent random variables (i)  $X \sim Pois(\mu)$ and (ii) $Y_i \sim Pois(\lambda),\;i\in{1,2}$.Question : Can we upper-bound the following?$$\mathbb{P}\big(X\geq\max(Y_1, Y_2)\big)$$
Probability of random variable $X$ less than $max(Y_i)$
reference request;pr.probability;randomness;upper bounds