Theoretical Distributions: Some Special Discrete Distributions

If the number of incoming buses per minute at a bus terminus is a random variable having a Poisson distribution with $\lambda =0.9$, find the probability that there will be : at least $14$ incoming buses during a period of $11$ minutes.

If the number of incoming buses per minute at a bus terminus is a random variable having a Poisson distribution with $\lambda =0.9$, find the probability that there will be : fewer than $10$ incoming buses during a period of $8$ minutes.

If the number of incoming buses per minute at a bus terminus is a random variable having a Poisson distribution with $\lambda =0.9$, find the probability that there will be : exactly $9$ incoming buses during a period of $5$ minutes.

In a Poisson distribution if $P(X=2)=P(X=3)$ then, the value of its parameter $\lambda$ is :

If, in a Poisson distribution $P(X=0)=k$ then the variance is