If a random variable $X$ follows a Poisson distribution with a mean value of $5$,then the probability that $X < 3$ is:

State whether the following table represents a probability distribution of a random variable $X$. Give reasons for your answer.

$X$	$0$	$1$	$2$
$P(X)$	$0.4$	$0.4$	$0.2$

The probability distribution of a random variable $X$ is as follows. Then the mean of $X$ is

$X = x_{i}$	$-2$	$-1$	$0$	$1$	$2$
$P(X = x_{i})$	$k^2 / 3$	$k^2$	$2k^2 / 3$	$k / 2$	$k / 2$

If the probability of a bad reaction from a vaccination is $0.01$, then the probability that exactly two out of $300$ people will get a bad reaction is

If the mean of a Poisson variate $X$ is $1$,then $\sum_{r=0}^{\infty}|r-1| P(X=r)=$

Let $X$ be a continuous random variable with the probability density function (p.d.f.) given by $f(x) = \begin{cases} kx, & 0 \leq x < 1 \\ k, & 1 \leq x < 2 \\ -kx + 3k, & 2 \leq x < 3 \\ 0, & \text{otherwise} \end{cases}$. Find $P(2 < X \leq 3)$.