The probability distribution of a discrete random variable X is

$\mathrm{X}$	0	1	2	3	4
$\mathrm{P(X=}x)$	$\mathrm{2k}$	$\mathrm{k}$	$\mathrm{2k}$	$\mathrm{4k}$	$\mathrm{k}$

If $\mathrm{a}=\mathrm{P}(x<3)$ and $\mathrm{b}=\mathrm{P}(2 \leq \mathrm{X}<4)$, then

If a random variable $X$ has the p.d.f. $f(x)=\left\{\begin{array}{cc}\frac{\mathrm{k}}{x^2+1} & , \text { if } 0< x< \infty \\ 0 & , \text { otherwise }\end{array}\right.$ then c.d.f. of X is

If a random variable $X$ follows the Binomial distribution $\mathrm{B}(33, \mathrm{p})$ such that $3 \mathrm{P}(\mathrm{X}=0)=\mathrm{P}(\mathrm{X}=1)$, then the variance of X is

If a discrete random variable X is defined as follows

$\mathrm{P}[\mathrm{X}=x]=\left\{\begin{array}{cl}\frac{\mathrm{k}(x+1)}{5^x}, & \text { if } x=0,1,2 \ldots \ldots . \\ 0, & \text { otherwise }\end{array}\right.$

then $\mathrm{k}=$