Let [math]X[/math] be a random variable with distribution function [math]m_X(x)[/math] defined by

[[math]] m_X(-1) = 1/5,\ \ m_X(0) = 1/5,\ \ m_X(1) = 2/5,\ \ m_X(2) = 1/5\ . [[/math]]

• Let [math]Y[/math] be the random variable defined by the equation [math]Y = X + 3[/math]. Find the distribution function [math]m_Y(y)[/math] of [math]Y[/math].
• Let [math]Z[/math] be the random variable defined by the equation [math]Z = X^2[/math]. Find the distribution function [math]m_Z(z)[/math] of [math]Z[/math].