Savida Renni

The graph of an even function is symmetric w.r.t. Y-axis. Is  is an even function.

The graph of an odd function has rotational symmetry w. r. t. the origin. X is an odd function.

 = xΙxΙ  =   in  (0,)  and -  in (-, 0).

Therefore, f(-x) =    in  (0,)  and -  in (-, 0).

x	1	2	3	4
	1	4	9	16
-	-1	-4	-9	-16

The half part of graph comes in first quadrant and the other half comes in the fourth quadrant . So, it is neither odd nor even.

Answer to Q.5:

f(x) = 3/4 () ,

       = 0 , otherwise.

E(x)= 3/4 dx

      =3/4(

      = 1.

Var(x) =

   =

Q.6)  The two regression equations are,

       2X-3Y+6=0...............(1)   and

       4Y-5X-8=0.................(2)

     a)   mean of X and mean of Y lies at the intersection of both the lines of regression equations.

Solving these two equations,

(1) x5  + (2)x 2 gives,

X=0, and Y=2

Thus, the mean of X=0  and mean of Y =2

b)  From (1), Y=2/3 X + 2

              b_{yx   =2/3}

From (2), X =4/5 Y - 8/5

             b_{xy  = 4/5}

_{r2 =} b_{yx   .bxy}

   _{=2/3  x 4/5}

  _=8/15

_{so, r= 0.73, the correlation coefficient between X and Y}

_{r is positive, since ^bxy  and ^byx are positive.}