If the probability density function of a continuous random variable $X$ is $f(x) = \frac{x^3}{3}$ for $-1 < x < 2$,and $f(x) = 0$ otherwise,then the cumulative distribution function $F(x)$ for $-1 < x < 2$ is:

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

$X$	$0$	$1$	$2$	$3$	$4$
$P(X)$	$0.1$	$0.5$	$0.2$	$-0.1$	$0.3$

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 $\text{Var}(X)$.

Two persons $A$ and $B$ play a game by throwing two dice. If the sum of the numbers appeared on the two dice is even, $A$ will get $\frac{1}{2}$ point and $B$ will get $\frac{1}{2}$ point. If the sum is odd, $A$ will get one point and $B$ will get no point. The arithmetic mean of the random variable of the number of points of $A$ is

The variance of the following probability distribution is:

$x$	$0$	$1$	$2$
$P(X)$	$\frac{9}{16}$	$\frac{3}{8}$	$\frac{1}{16}$

The range of a random variable $X$ is $\{0, 1, 2\}$. If $P(X=0) = 3C^3$,$P(X=1) = 4C - 10C^2$,and $P(X=2) = 5C - 1$,then the value of $C$ is