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Let \(X\) be a random variable following an exponential distribution with parameter \(\lambda\). What is the expression of its probability density function \(f\) on \([0, +\infty)\)?
\(f(x) = \lambda e^{-\lambda x}\)
\(f(x) = e^{-\lambda x}\)
\(f(x) = 1 - e^{-\lambda x}\)
\(f(x) = \frac{1}{\lambda} e^{-\lambda x}\)
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