If a die is thrown at random,then the expectation of the number on it is

The probability distribution of a random variable $X$ is given below:

$x$	$1$	$2$	$3$	$4$	$5$	$6$
$P(X=x)$	$a$	$a$	$a$	$b$	$b$	$0.3$

If the mean of $X$ is $4.2$, then $a$ and $b$ are respectively equal to:

The probability distribution of a discrete random variable $X$ is given by the table below:

$X$	$0$	$1$	$2$	$3$	$4$
$P(X=x)$	$2k$	$k$	$2k$	$4k$	$k$

If $a = P(X < 3)$ and $b = P(2 < X < 4)$,then:

The probability distribution of a random variable $X$ is given by the following table:

$X = x_i$	$3$	$5$	$7$	$9$
$P(X = x_i)$	$k$	$2k$	$3k$	$4k$

Then the standard deviation of $X$ is

$A$ 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

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

$X=x_i$	$-2$	$-1$	$0$	$1$	$2$
$P(X=x_i)$	$1/6$	$k$	$1/4$	$k$	$1/6$

The variance of this random variable is