For a probability distribution $P(x) = \frac{c}{3} \binom{4}{x}$,where $x = 1, 2, 3, 4$,the value of $c$ is . . . . . . .

Let $X$ represent the difference between the number of heads and the number of tails obtained when a coin is tossed $6$ times. What are the possible values of $X$?

If the probability distribution of a random variable $X$ is as follows,then the mean of $X$ is:

$X = x_i$	$-1$	$0$	$1$	$2$
$P(X = x_i)$	$k^3$	$2k^3 + k$	$4k - 10k^2$	$4k - 1$

If a drunkard person tries to take a step,then it will be a forward or backward step with probabilities $\frac{1}{4}$ and $\frac{1}{2}$ respectively,or he will remain in his 'as it is' position. If he tries to take a step $5$ times,then find the probability that he will be one step away from the initial position.

At a telephone enquiry system,the number of phone calls regarding relevant enquiries follows a Poisson distribution with an average of $5$ phone calls during $10$-minute time intervals. The probability that there is at most one phone call during a $10$-minute time period is:

If the probability distribution of a random variable $X$ is given by:

$X = x_i$	$0$	$1$	$2$	$3$
$P(X = x_i)$	$\frac{1}{8}$	$\frac{3}{8}$	$3K$	$K$

Find the variance of $X$.