The probability distribution of random variable $X$ is given by:

$X$	$1$	$2$	$3$	$4$	$5$
$P(X)$	$K$	$2K$	$2K$	$3K$	$K$

Let $p=P(1 < X < 4 \mid X < 3)$. If $5p = \lambda K$,then $\lambda$ is equal to .... .

The random variable $X$ has a probability distribution $P(X)$ of the following form,where $k$ is some number:
$P(X) = \begin{cases} k, & \text{if } x=0 \\ 2k, & \text{if } x=1 \\ 3k, & \text{if } x=2 \\ 0, & \text{otherwise} \end{cases}$
Determine the value of $k$.

If $X$ is a Poisson variate such that $P(X=1) = 2P(X=2)$,then $P(X=3)$ is equal to:

If a discrete random variable $X$ takes the values $1, 2, 3, 4$ such that $2P(X = 1) = 3P(X = 2) = P(X = 3) = 5P(X = 4)$, then $P(X = 4) = ...$ (in $61$)

If a random variable $X$ has the following probability distribution of $X$:

$X=x$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$
$P(X=x)$	$0$	$k$	$2k$	$2k$	$3k$	$k^2$	$2k^2$	$7k^2+k$

Then $P(X \geqslant 6) = $

From a lot of $20$ baskets,which includes $6$ defective baskets,a sample of $2$ baskets is drawn at random one by one without replacement. The expected value of the number of defective baskets is