$A$ random variable $X$ assumes values $1, 2, 3, \ldots, n$ with equal probabilities. If $\operatorname{Var}(X) = E(X)$,then $n$ is:

If $m$ and $\sigma^2$ are the mean and variance of the random variable $X$,whose distribution is given by:

$X=x$	$0$	$1$	$2$	$3$
$P(X=x)$	$\frac{1}{3}$	$\frac{1}{2}$	$0$	$\frac{1}{6}$

Then:

If a random variable $X$ has the following probability distribution, then its variance is

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

$A$ player tosses two coins. He wins $Rs. 1$ if $1$ head appears,$Rs. 2$ if $2$ heads appear. But he loses $Rs. 3$ if no head appears. The mean of the prize money is

For the following cumulative distribution function $F(x)$ of a random variable $X$,find $P(3 < X \leq 5)$.

$x$	$1$	$2$	$3$	$4$	$5$	$6$
$F(x)$	$0.2$	$0.37$	$0.48$	$0.62$	$0.85$	$1$

$A$ fair coin is tossed four times. $A$ person wins $Rs. 1$ for each head and loses $Rs. 1.50$ for each tail that turns up. From the sample space,calculate the different amounts of money one can have after four tosses and the probability of having each of these amounts.