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Children arrive at an ice-cream parlour as a non-homogeneous Poisson process with rate t, where t...

Children arrive at an ice-cream parlour as a non-homogeneous Poisson process with rate t, where t is the time measured in hours between noon and 6pm. Justify all your answers and write down the derivations in detail.

(i) If we know that at least one child arrived in the first hour, what is the density function of the arrival time of the child who arrived first? [2 marks]

(j) Assume that each child independently buys a geometric random number of ice creams with mean 2. What is the mean and variance of the number of ice cream sold before 2pm? [2 marks

Math   Statistics-And-Probability   
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