If three fair coins are tossed,then the variance of the number of heads obtained is

If a random variable $x$ has the probability distribution as follows:

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

Then $P(3 < x \leq 6)$ is equal to:

If $6$ is the mean of a Poisson distribution,then $P(X \geq 3)=$

$A$ player tosses two coins. He wins $Rs. 10$ if $2$ heads appear,$Rs. 5$ if one head appears,and $Rs. 2$ if no head appears. Find the variance of the winning amount.

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

$X = x$	$1$	$2$	$3$	$\dots$	$n$
$P(X = x)$	$\frac{1}{n}$	$\frac{1}{n}$	$\frac{1}{n}$	$\dots$	$\frac{1}{n}$

Then $\operatorname{Var}(X) = $

$A$ random variable $X$ has the range $\{0, 1, 2, \ldots\}$. If $P(X=r) = k(1+r) 3^{-r}$ for $r=0, 1, 2, \ldots$, where $k > 0$ is a real number, then $P(X=0) + P(X=1) + P(X=2) =$