IF a and b are any two constants , then prove that var `(ax+b)=a^(2 )var (x ).`

if a and b are any two constants, then prove that Var (aX+b)=a^2Var(X) .

If a and b are constants, then show that var (ax+b)=a^2 var (x) .

Prove that Var (a+bx)= b^(2) Var(x)

If Y = a + bx, a, b be two real constants, then prove that Range (y) = |b|, Range (x).

answer any one question : (ii) if X and Y are two independent variables , then rove that var(aX+bY ) =a^2 var (X) +b^2 var (Y) , where a and b are constants

If a and b are two arbitrary constants, then prove that the straight line (a-2b)x+(a+3b)y+3a+4b=0 will pass through a fixed point. Find that point.

If X and Y are two independent variables, then prove that var(aX+bY)=a^2var(X)+b^2var(Y) , where a and b are constants.

For any two sets A and B, Prove that A cup (Acap B) = A.

If the simultaneous linear equations in two variables a^(2)x+b^(2)y=1 " and " x/(a^(2)+1)+y/(b^(2)+1)=k , where a ne b and a, b, k are constants have no solution, then prove that a^(2)+b^(2)+1=0 .

If a is a constant prove that (i) var(a)=0 (ii) var (aX)=a^(2)var(X) (iii) Var(ax+b)=a^(2)var(X)