Variance Transformation of a Discrete Random Variable
Let X be a discrete random variable with the following probability mass function: – P(X = 0) = 0.25 – P(X = 1) = 0.50 – P(X = 2) = 0.25 Using the rules for linear transformations, calculate Var(4X – 3).
Variance Transformation in Linear Functions
Let X be a random variable with variance \(\mathrm{Var}(X)\). Show that for any constants \(a\) and \(b\), the variance of the linear transformation \(aX + b\) is given by \(\mathrm{Var}(aX+b)=a^2\mathrm{Var}(X)\).