Find the mean number of heads in three tosses of a fair coin. (in $.5$)

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

$X = x$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
$P(X = x)$	$0.15$	$0.23$	$k$	$0.10$	$0.20$	$0.08$	$0.07$	$0.05$

For the events $E = \{x : x \text{ is a prime number}\}$ and $F = \{x : x < 4\}$, then $P(E \cup F) = $

Two dice are rolled. If a random variable $X$ is defined as the absolute difference of the two numbers that appear on them, then the mean of $X$ is

If the probability distribution of a random variable $X$ is as follows, then the variance of $X$ is
$\begin{array}{|c|c|c|c|c|}\hline X=x & 2 & 3 & 5 & 9 \\\hline P(X=x) & K & 2 K & 3 K^2 & K^2 \\\hline\end{array}$

The distribution of a random variable $X$ is given below. The value of $k$ is:

$X = x$	$-2$	$-1$	$0$	$1$	$2$	$3$
$P(X = x)$	$\frac{1}{10}$	$k$	$\frac{1}{5}$	$2k$	$\frac{3}{10}$	$k$

$A$ random variable $X$ has the following probability density function (p.d.f.):
$f(x) = kx(1-x), 0 \leqslant x \leqslant 1$
If $P(X > a) = \frac{20}{27}$,then find the value of $a$.