Question: The time (in years) until a certain machine requires repairs is a random variable t with probability density function defined by (a) Find the probability

The time (in years) until a certain machine requires repairs is a random variable t with probability density function defined by f(t) = 5 112 (1/2) for tin [1, 25].

(a) Find the probability that no repairs are required in the first three years by finding the probability that a repair will be
needed in years 4 through 25.
(b) Find the expected value for the number of years before the machine requires repairs.
(c) Find the standard deviation.

f(t) = 5 112 (1/2) for tin [1, 25].

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