If a variable takes values $0, 1, 2, ..., n$ with frequencies proportional to the binomial coefficients $^nC_0, ^nC_1, ..., ^nC_n$,find the mean of the distribution.

For the following probability distribution of a random variable $X$, the Expected value $E(X)$ and Variance $Var(X)$ of $X$ are respectively:

$X=x$	$1$	$2$	$3$
$P(X=x)$	$1/5$	$2/5$	$2/5$

The probability distribution of a random variable $X$ is as follows. Then the mean of $X$ is

$X = x_{i}$	$-2$	$-1$	$0$	$1$	$2$
$P(X = x_{i})$	$k^2 / 3$	$k^2$	$2k^2 / 3$	$k / 2$	$k / 2$

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

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

The p.m.f. of a random variable $X$ is $P(x) = \begin{cases} \frac{2x}{n(n+1)}, & x = 1, 2, 3, \ldots, n \\ 0, & \text{otherwise} \end{cases}$,then $E(X)$ is

In a game,a man wins $Rs. 100$ if he gets $5$ or $6$ on a throw of a fair die and loses $Rs. 50$ for getting any other number on the die. If he decides to throw the die either until he gets a five or a six or to a maximum of three throws,then his expected gain/loss (in rupees) is