a) If f(y) is a probability density function, then both f(y) ≥ 0 for all y in its support, and the integral of f(y) over its entire support should be 1. eˣ > 0 for all real x, so the first condition is met. We have
so both conditions are met and f(y) is indeed a PDF.
b) The probability P(Y > 4) is given by the integral,