If the mean of the distribution is $2.6$,then the value of $y$ is:

Variate $x$	$1$	$2$	$3$	$4$	$5$
Freq $f$ of $x$	$4$	$5$	$y$	$1$	$2$

The sum of two positive integers is $100$. The probability that their product is greater than $1000$ is

The mean and variance of eight observations are $9$ and $9.25,$ respectively. If six of the observations are $6, 7, 10, 12, 12,$ and $13,$ find the remaining two observations.

The mean and variance of the data $4, 5, 6, 6, 7, 8, x, y$ where $x < y$ are $6$ and $\frac{9}{4}$ respectively. Then $x^{4} + y^{2}$ is equal to

The average income of individuals in one group is $\bar{x}$ and the average income of another group is $\bar{y}$. If the ratio of the number of individuals in both groups is $4:3$,what is the average income of the combined group?

The mean of a set of $30$ observations is $75$. If each observation is multiplied by a non-zero number $\lambda$ and then each of them is decreased by $25$,their mean remains the same. The value of $\lambda$ is equal to