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- The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponential distribution with mean 1000 cfs (cubic feet per second). b) What water-pumping capacity should the station maintain during early afternoons so that the probability that demand will be below the capacity on a randomly selected day is 0.995? c) Of the three randomly selected afternoons, what is the probability that on at least two afternoons the demand will exceed 700 cfs?Suppose that the unknown X is uniformly distributed between 0 and 1. What is the expected value of (X^4+2x+1)?If the random variable X is exponentially distributed with parameter λ = 4, then the probability P(X ≤ 0.25) is equal to: