Poisson Distribution

If a random variable $X$ follows a Poisson distribution such that $P(X=1)=3 P(X=2)$, then $P(X=3)=$

In a poisson distribution mean is $16$, then standard deviation is

If $f\left(x\right)=\lambda e^{-ax}(a>0)$ for $0\le x<\infty$is a prabability density, then $\lambda$ is equal to

A random variable $X$ has poisson distribution with mean$2.$Then, $P(X>1.5)$ equals

If $X$ is a poisson variate with $P\left(X=0\right)=0.8,$ then the variance of $X$ is

If $X$ is a poisson variate such that $P\left(X=1\right)=P\left(X=2\right)$, then $P(X=4)$ is equal to

For a poisson variate $X$, if $P\left(X=2\right)=3P\left(X=3\right)$, then the mean of $X$ is

At a telephone enquiry system, the number of phone calls regarding relevant enquiry follows a Poisson distribution with an average of $5$ phone calls during $10$ min time intervals. The probability that there is at the most one phone call during a $10$ min time period, is

At a telephone enquiry system the number of phone calls regarding relevant enquiry follow Poisson distribution with a average of $5$ phone calls during $10-$minute time intervals. The probability that there is at the most one phone call during a $10-$minute time period is