Final answer:
The correct PDF is f(y) = e^(-y) and its support is y > 0, which is found by differentiating the given CDF F(y) and determining where the PDF is positive.
Step-by-step explanation:
To find the probability density function (PDF) and its support from the given cumulative distribution function (CDF), P(Y < y) = F(y), we need to differentiate the CDF to get the PDF. The support of a random variable is the set of values where the PDF is positive.
Option c) PDF: f(y) = e^(-y); Support: y > 0 is the correct choice here. To see why, take the derivative of the CDF F(y) = 1 - e^(-y) with respect to y. The derivative, which gives us the PDF, is f(y) = e^(-y). Furthermore, the CDF implies that P(Y < 0) = 1 - e^(0) = 0, which means that the PDF is positive only when y > 0, thus the support is y > 0.