$A$ random variable $X$ has the following probability distribution:
$X$: $1, 2, 3, 4$
$P(X)$: $0.2, 0.4, 0.3, 0.1$
The mean and variance of $X$ are respectively:

$A$ bag contains $4$ white and $6$ black balls. Three balls are drawn at random from the bag. Let $X$ be the number of white balls among the drawn balls. If $\sigma^{2}$ is the variance of $X$,then $100 \sigma^{2}$ is equal to.

$A$ person who tosses an unbiased coin gains two points for turning up a head and loses one point for a tail. If three coins are tossed and the total score $X$ is observed, then the range of $X$ is

The probability distribution of $X$ is
$\begin{array}{|c|c|c|c|c|} \hline X & 0 & 1 & 2 & 3 \\ \hline P(X) & 0.3 & k & 2k & 2k \\ \hline \end{array}$
Find the value of $k$.

$A$ random variable $X$ takes the values $0, 1, 2, 3, \dots$ with probability $P(X=x) = k(x+1)\left(\frac{1}{5}\right)^x$,where $k$ is a constant. Then $P(X=0)$ is

$A$ die is thrown repeatedly until a six comes up. What is the sample space for this experiment?