Let the cumulative distribution function (CDF) of random variable x be f(x) = { 1 - e⁻ˣ, x>0; 0, x<=0 }
a) Find P(-1 < x < 1)
b) Find the probability density function (PDF) of x
c) Let y = max{1, x}, find the CDF of y.

a) e⁻¹ - e⁻¹
b) f(x) = e⁻ˣ
c) F_Y(y) = { 0, y <= 1; 1 - e⁻ʸ, y > 1 }