Suppose the number of people who get infected to Corona virus everyday in a village has Poisson distribution and on average 10 people get infected per day. What is the probability that from day 1 to day 10, the number of people who get infected each day is increasing?
Note: Obviously the question is talking about 10 integers like $x_0≤x_1≤x_2≤...≤x_9$ and since each day is independent of the other, I think calculating the multiplication of $P(X=x_0).P(X=x_1)...P(X=x_9)$ would help. But I am stuck from here on.
$$P(\text{Increasing cases}) = \sum_{x_0\leq ...\leq x_{0} \\ x_0 + x_1 ...+x_{9} \leq \text{population}} P(X=x_0).P(X=x_1)...P(X=x_9)$$