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Let {Xj} ∞ j=1 be a collection of i.i.d. random variables uniformly distributed on [0, 1]....

Let {Xj} ∞ j=1 be a collection of i.i.d. random variables uniformly distributed on [0, 1]. Let N be a Poisson random variable with mean n, and consider the random points {X1 , . . . , XN }.

b. Let 0 < a < b < 1. Let C(a,b) be the number of the points {X1 , . . . , XN } that lies in (a, b). Find the conditional mass function of C(a,b) given that N = j.

b. Identify the distribution of C(a,b) (including values of any parameters)

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