Problem 5. (+20pts) The time to failure X in hours of a piece of electronic equipment has the density function 1 _L x) = Me 25003 x Z 0, 0, elsewhere. (a) Verify that f (as) is a valid density function. (h) Find the cumulative distribution function F(a:) of X. (c) Determine the probability that the component (and thus the DVD player) lasts more than 900 hours before the component needs to be replaced. (d) Determine the probability that the cemponent fails before 2500 hours