The p.d.f. of a continuous random variable $X$ is given by $f(x) = \frac{1}{2}$ if $0 < x < 2$ and $f(x) = 0$ otherwise. If $a = P(X < \frac{1}{2})$ and $b = P(X > \frac{3}{2})$,then the relation between $a$ and $b$ is:

$A$ random variable $X$ has the following probability distribution:

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

Find the value of $P(0 < X < 6)$.

Let $X$ be the random variable taking values $1, 2, \ldots, n$ for a fixed positive integer $n$. If $P(X=k) = \frac{1}{n}$ for $1 \leq k \leq n$,then the variance of $X$ is

$A$ random variable $X$ has the following probability distribution:

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

Then $P(X > 2)$ is equal to:

$A$ student studies for $X$ number of hours during a randomly selected school day. The probability distribution of $X$ is given by the following form,where $k$ is a constant:
$P(X=x) = \begin{cases} 0.2, & \text{if } x=0 \\ kx, & \text{if } x=1 \text{ or } 2 \\ k(6-x), & \text{if } x=3 \text{ or } 4 \\ 0, & \text{otherwise} \end{cases}$
The probability that the student studies for at most two hours is:

The cumulative distribution function $F(x)$ of a discrete random variable $X$ is given by the following table:

$X = x$	$-1$	$0$	$1$	$2$
$F(X = x)$	$0.3$	$0.7$	$0.8$	$1$

Then $E(X^2) = $