If $X$ is a Poisson variate satisfying the condition $3 P(X=2)=P(X=4)$, then find $P(X=6)$.

$A$ random variable $X$ has the probability distribution given below. Its variance is:

$X$	$1$	$2$	$3$	$4$	$5$
$P(X=x)$	$K$	$2K$	$3K$	$2K$	$K$

The probability distribution of a discrete random variable $X$ is given by the following table:

$X = x$	$0$	$1$	$2$	$3$	$4$
$P(X = x)$	$k$	$2k$	$4k$	$2k$	$k$

Then the value of $P(X \leq 2)$ is:

For the probability distribution given by

$x = x_{i}$	$0$	$1$	$2$
$P_{i}$	$\frac{25}{36}$	$\frac{5}{18}$	$\frac{1}{36}$

the standard deviation $(\sigma)$ is

State which of the following is not the probability distribution of a random variable. Give reasons for your answer.

$Z$	$3$	$2$	$1$	$0$	$-1$
$P(Z)$	$0.3$	$0.2$	$0.4$	$0.1$	$0.05$

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 $\text{Var}(X)$.