Given below is the distribution of a random variable $X$:

$X=x$	$1$	$2$	$3$	$4$
$P(X=x)$	$\lambda$	$2\lambda$	$3\lambda$	$4\lambda$

If $\alpha=P(X < 3)$ and $\beta=P(X>2)$,then $\alpha: \beta=$

The probability distribution of a discrete random variable $X$ is given by the table below:

$X$	$0$	$1$	$2$	$3$	$4$
$P(X=x)$	$2k$	$k$	$2k$	$4k$	$k$

If $a = P(X < 3)$ and $b = P(2 < X < 4)$,then:

The c.d.f. $F(x)$ associated with the p.d.f. $f(x)$ is given by:
$f(x) = \begin{cases} 12x^2(1-x), & \text{if } 0 < x < 1 \\ 0, & \text{otherwise} \end{cases}$

The probability function of a random variable $X$ is given by $P(X=k)=c k^2$,where $c$ is a constant and $k \in\{0,1,2,3,4\}$. If $\sigma^2$ is the variance of $X$ and $\mu$ is the mean of $X$,then $\sigma^2+\mu^2=$

For the random variable $X$ with the probability distribution given by the table:

$X = x$	$0$	$1$	$2$	$3$
$P(X = x)$	$K$	$K + \frac{1}{7}$	$2K$	$\frac{2}{5}$

The mean of $X$ is:

In a Poisson distribution, if $\frac{P(X=5)}{P(X=2)}=\frac{1}{7500}$ and $\frac{P(X=5)}{P(X=3)}=\frac{1}{500}$, then the mean of the distribution is