question3 3. [5 points] Suppose that the number of customers arriving at the Woe

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question3

3. [5 points] Suppose that the number of customers arriving at the Woeri Bank follows a Poisson process with a rate of Aw 0.5 per minute, the number of customers arriving at the Hana Bank follows a Poisson process with a rate of A 0.2 per minute, the two Poisson processes kth customer at the Woori Bank and H be the waiting time to have the kth customer at the Hana Bank. Fi are independent. LetW be the waiting time to have the nd the probability distribution of the random variabte and explain why

Explanation / Answer

3.28

fX(x) = e-x

Here CDF of exponential randomvariable

F(x) = 1 - e-x

Pr(3X < 5) = Pr(X < 5/3) = 1 - e-5/3 = 0.81111

(b) Pr(3X < Y) = 1 - e-Y/3

(c) Here F(Y0 = 1 -e-Y/3

f(y) = dF(y)/dy = 1/3e-y/3

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