CDF and Tail Probability of the Exponential Distribution

Let $X \sim \text{Exponential}(\lambda)$ with PDF $f(x) = \lambda e^{-\lambda x}$ for $x \geq 0$.

(a) Derive the CDF $F(x) = P(X \leq x)$.

(b) If $\lambda = \frac{1}{2}$, compute $P(X > 3)$.