Let X be a continuous random variable with probability density function f and assume that a ≠ 0 and b are two real numbers.

(i) Show that the probability density fY of the variable Y = aX + b is given by the formula

(ii) If the probability density of X is given by

find the density function of Y = ???? + ????X, where???? > 0 and ???? ∈ ℝ are two real constants.

Transcribed Image Text:

fy(y)= =lar (v=b). -b a