In the notation below,X is the random variable,c is a constant,and V refers to the variance.Which of the following laws of variance is not true? A)V(c)= 0 B)V(X + c)= V(X)+ c C)V(cX)= c² V(X) D)None of these choices.

Question

Quizplus · Accepted Answer

The correct formula for the variance of X + c is V(X + c) = V(X), where c is a constant. Therefore, the statement "V(X + c) = V(X) + c" is not true, making option B incorrect.

Option A is true because the variance of a constant is always zero. Option C is also true because for the constant c, we have V(cX) = c^2 V(X), which can be simplified to c²× 0. This gives V(cX) = 0, making option C correct. Thus, the correct answer is B.

In the Notation Below,X Is the Random Variable,c Is a Constant,and