Problem #1 (20 points) – An Discrete Distribution

A total of m balls are to be randomly selected, without replacement, from

an urn that contains n ≥ m balls numbered 1 through n. If X is the smallest

numbered ball selected, determine (in terms of n and m) the range set of X,

the probability mass function (pmf) of X (in terms of n, m and x) and the

cumulative distribution function (cdf) of X (in terms of n, m and x). You

may look up any binomial coefficient identity needed to simply the cdf, or

you may use Maple to simply the sum.

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