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 $k=$

In a hospital, on an average if there are $35$ births in a week, then the probability that there will be less than $3$ births in a day is:

In a meeting,$70 \%$ of the members favour and $30 \%$ oppose a certain proposal. $A$ member is selected at random and we take $X=0$ if he opposed,and $X=1$ if he is in favour. Find $E(X)$ and $\text{Var}(X)$.

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

For the following cumulative distribution function $F(x)$ of a random variable $X$,find $P(3 < X \leq 5)$.

$x$	$1$	$2$	$3$	$4$	$5$	$6$
$F(x)$	$0.2$	$0.37$	$0.48$	$0.62$	$0.85$	$1$

Three fair coins,each numbered $1$ and $0$,are tossed simultaneously. The variance $\operatorname{Var}(X)$ of the probability distribution of the random variable $X$,where $X$ is the sum of the numbers on the uppermost faces,is: