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 find $P(0 < X \le 2)$.

Two cards are drawn at random from a box which contains $5$ cards numbered $1, 1, 2, 2, 3$. If $X$ denotes the sum of the numbers on the two cards, then the expected value of $X$ is...

The mean of the numbers obtained on throwing a die having written $1$ on three faces,$2$ on two faces,and $5$ on one face is

The random variable $X$ has the following probability distribution:
| $X$ | $8$ | $12$ | $16$ | $20$ | $24$ |
|---|---|---|---|---|---|
| $P(X)$ | $K$ | $\frac{1}{6}$ | $\frac{3}{8}$ | $2K$ | $\frac{1}{12}$ |
Then the value of $K$ is:

In a meeting,$70 \%$ of the members favour and $30 \%$ oppose a certain proposal. $A$ member is selected at random. We take $X=0$ if he opposes the proposal and $X=1$ if the member is in favour. Then the variance of $X$ is:

$A$ random variable $X$ has the following probability distribution:

$X$	$0$	$1$	$2$	$3$	$4$	$5$	$6$
$P(X)$	$k$	$3k$	$5k$	$7k$	$9k$	$11k$	$13k$

Then find $P(X \ge 2)$.