Maximum Likelihood Estimation

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The urn contains an unknown number of marbles, each a different color. Randomly select marbles one at a time (with replacement) until a repeat occurs.

The concept of a maximum likelihood estimate is illustrated using a discrete example. An urn contains

n

different colored marbles. Marbles are selected one at a time at random with replacement until one marble has been selected twice. What is the maximum likelihood estimate of the number of marbles in the urn?