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
a. Find 
.
b. Find the cumulative distribution function of X.
c. Let ?1 = 2, ?2 = 1, and p = 0.5. Find P(X ? 2).
d. Let ?1 = 2, ?2 = 1, and p = 0.5. Given that P(X ? 2), find the probability that mass 1 was selected.
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