Consider a random variable ?x with the following values and the corresponding probabilities:
{Δx = 1, p(Δx = 1) = .3},
{Δx = -0.5, p(Δx = -0.5) = .2},
{Δx = .2, p(Δx = .2) = .5}.
(a) Calculate the mean and the variance of this random variable.
(b) Change the mean of this random variable to .05 by subtracting an appropriate constant from ?x. That is, calculate
?y = ?x - μ
Such that ?y has mean .05.
(c) Has the variance changed?
(d) Now do the same transformation using a change in probabilities, so that again the variance remains constant.
(e) Have the values of ?x changed?