Customers arrive as a rate-ten Poisson process. Independently each is male or female with probability 1/2. Let N(t) count all arrivals,M(t) males,and S₂ be the second female-arrival time. Which is NOT true?
Thinning makes female and male processes rate five,proving the Gamma(2,5) density in A. Given one male arrival by time 1,its time is uniform on (0,1),so the chance of none before 1/3 is **2/3**,not 1/3. C follows from Poisson variance and mean;D uses covariance 10t and product of means 200t². Thus **B**.
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