For the probability distribution of a discrete random variable $X$ as given below, then mean of $X$ is

X = x	-2	-1	0	1	2	3
P(X = x)	$$ \frac{1}{10} $$	$$ K+\frac{2}{10} $$	$$ K+\frac{3}{10} $$	$$ K+\frac{3}{10} $$	$$ K+\frac{4}{10} $$	$$ K+\frac{2}{10} $$

In a random experiment, two dice are thrown and the sum of the numbers appeared on them is recorded. This experiment is repeated 9 times. If the probability that a sum of 6 appears atleast once is $P_1$ and a sum of 8 appears atleast once is $P_2$, then $P_1: P_2=$

If the line segment joining the points $(1,0)$ and $(0,1)$ subtends an angle of $45^{\circ}$ at a variable point $P$, then the equation of the locus of $P$ is

If the origin is shifted to a point $P$ by the translationd axes to remove the $y$-term from the equation $x^2-y^2+2 y-1=0$, then the transformed equation of it is