Radioactive mass 1 emits particles at a mean rate of 1, per second, and radioactive mass 2 emits particles at a mean rate of 2 per second. Mass 1 is selected with probability p, and mass 2 is selected with probability 1 - p. Let X be the time at which the first particle is emitted. It can be shown that X has a mixed exponential distribution with probability density function SPhieh+(1- p)Àze* S(x) = x > 0 a. Find Hx- b. Find the cumulative distribution function of X. C. Let 11 = 2, 12 = 1, and p = 0.5. Find P(X < 2). d. Let X, = 2, X, = 1, and p = 0.5. Given that P(X < 2), find the probability that mass 1 was selected.

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