Radioactive mass 1 emits particles at a mean rate of

Radioactive mass 1 emits particles at a mean rate of λ1per second, and radioactive mass 2 emits particles at a mean rate of λ2per 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 μX.

b. Find the cumulative distribution function of X.

c. Let λ1 = 2, λ2 = 1, and p = 0.5. Find P(X ≤ 2).

d. Let λ1 = 2, λ2 = 1, and p = 0.5. Given that.

P(X ≤ 2), find the probability that mass 1 was selected.

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