1 Let X be the random variable with distribution function pX

(1) Let X be the random variable with distribution function p_X(x) defined by p_X(-1) = 1/5, p_X(0) = 1/5, p_X(1) = 2/5, p_X(2) = 1/5.

(a) let Y be the random variable defined by he equation Y = X + 3. Find the distribution function p_Y(y) of Y.

(b) Let Z be the random variable defined by the equation Z = X². Find the distribution function p_Z(z) of Z.

Solution

a)PY(-1)=P(2)=2+3=5; PY(0)=P(3)=3+3=6;PY(1)=P(4)=4+3=7

B)PZ(-1)=P(1)=1; PZ(0)=P(0)=0; PZ(1)=P(1)=1