The probability distribution of a random variable is given by 

$x$	$0$	$1$	$2$	$3$
$P\left(x\right)$	$p_1$	$p_2$	$p_3$	$p_4$

If $p_1+p_2+p_3=0.8\text{ and }{p}_2+p_3+p_4=0.9$, then

A random variable $X$ has the following probability distribution 

Determine $P(1<x\le 3)$.

A probability distribution is listed below

Find the value of $k$.

A die is rolled. A random variable $X$ is as follows:

$X\left(x\right)=\left\{\begin{array}{l}1,\text{ if the outcome }x\text{ is an even number}\\ 0,\text{ if the outcome }x\text{ is an odd number}\end{array}\right.$