Suppose Var[X]=4, Var[Y]=1,and Cov [X,Y]= -1 .
calculate Var [X-2Y+10]
Formula used:
Cov(aX+b, cY+d) = ac Cov(X,Y)
V(aX+bY)= a2 V(X) + b2 V(Y) + 2ab Cov(X,Y)
Now,
V(X-2Y+10)= V(X) + V(-2Y+10) + 2Cov(X, -2Y+10)
= V(X) + (-2)2 V(Y) + 2*(-2) Cov(X,Y)
=4 + 4*1 - 4*(-1)
=4 + 4 + 4
=12
Suppose Var[X]=4, Var[Y]=1,and Cov [X,Y]= -1 . calculate Var [X-2Y+10]
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