The probability distribution of a random variable $X$ is given below.

$X = x$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$
$P(x)$	$0.01$	$0.10$	$0.26$	$0.33$	$0.18$	$0.06$	$K$	$0.04$

Then $P(X \geq 3) - P(X < 6) =$

An observer counts $240$ vehicles per hour at a specific location on a highway. Assuming that the arrival of vehicles at the location follows a Poisson distribution,the probability that more than two vehicles arrive over a $30 \text{ sec}$ time interval is

Two numbers are selected at random from the first six positive integers. If $X$ denotes the larger of the two numbers,then $\operatorname{Var}(X) = $

$A$ random variable $X$ has the range $\{0, 1, 2, \ldots\}$. If $P(X=r) = k(1+r) 3^{-r}$ for $r=0, 1, 2, \ldots$,where $k > 0$ is a real number,then $P(X=0) + P(X=1) + P(X=2) =$

If $X$ is a random variable with probability distribution $P(X=k) = \frac{(2k+3)c}{3^k}$,$k=0, 1, 2, \ldots, \infty$,then $P(X=3) =$

For the probability distribution given below,find $\operatorname{Var}(X)$.

$X$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$P(X=x)$	$0.07$	$0.2$	$0.3$	$k$	$0.07$	$0.04$	$0.02$