Final answer:
The probability density function for an exponential random variable t with a unit mean is f(t) = e^(-t). Option A) f(t) = e^(-t) is the correct answer.
Step-by-step explanation:
The question asks for the probability density function (pdf) of an exponential random variable with a unit mean (E{t}=1). In an exponential distribution, the mean μ is the reciprocal of the decay parameter m (μ = 1∕m). Since μ = 1 for this problem, m would also equal 1, which gives us the pdf formula f(t) = me-mt, where t ≥ 0.
Subsequently, we plug in m = 1 to get f(t) = e-t. From the given options, the correct probability density function is A) f(t) = e-t which matches our derived formula.