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. Then, the standard deviation of $X$ is

$X=x_i$	$2$	$3$	$5$	$7$	$12$
$P(X=x_i)$	$3k$	$k$	$k$	$2k$	$k$

$A$ player tosses $2$ fair coins. He wins ₹ $5$ if $2$ heads appear,₹ $2$ if one head appears,and ₹ $1$ if no head appears. Then the variance of his winning amount in ₹ is

The p.d.f. of a random variable $X$ is given by $f(x) = \frac{k}{\sqrt{x}}$ for $0 \leq x \leq 4$ and $f(x) = 0$ otherwise. Then $P(1 < X < 4) = $

$A$ player tosses two fair coins. He wins $Rs. 5$ if two heads appear, $Rs. 3$ if one head appears, and $Rs. 2$ if no head appears. The variance of the winning amount is:

If on an average $4$ customers visit a shop in an hour, then the probability that more than $2$ customers visit the shop in a specific hour is