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

Suppose that a book of $600$ pages contains $40$ print mistakes. Assume that these errors are randomly distributed throughout the book and the number of errors per page follows a Poisson distribution. The probability that all the $10$ pages selected at random have no print mistakes is

In a meeting,$70 \%$ of the members favour and $30 \%$ oppose a certain proposal. $A$ member is selected at random and we take $X=0$ if he opposed,and $X=1$ if he is in favour. Find $E(X)$ and $\text{Var}(X)$.

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 $P(X=3) =$

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

$X$	$0$	$1$	$2$	$3$	$4$	$5$	$6$
$P(X)$	$k$	$3k$	$5k$	$7k$	$9k$	$11k$	$13k$

Then find $P(X \ge 2)$.

$A$ 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 $a$.