If $P(X=x)=k\left(\frac{3}{8}\right)^{X}, x=1,2,3, \ldots$ is the probability distribution function of a discrete random variable $X$,then $k=$

$A$ fair $n$ $(n > 1)$ faced die is rolled repeatedly until a number less than $n$ appears. If the mean of the number of tosses required is $\frac{n}{9}$,then $n$ is equal to

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:

$A$ person draws a card from a pack of $52$ cards and replaces it. After shuffling,he draws a card again. If he repeats this process,what is the probability that he draws a red card for the first time on the third draw?

For the following probability distribution,find the expected value of $X$:

$x$	$0$	$1$	$2$	$3$	$4$	$5$
$P(x)$	$k$	$0.3$	$0.15$	$0.15$	$0.1$	$2k$

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

$X = x_i$	$0$	$1$	$2$	$3$	$4$
$P(X = x_i)$	$0.4$	$0.3$	$0.1$	$0.1$	$0.1$

Then the variance of $X$ is: