A bucket has three marbles.  Two are black and one is white.  You keep drawing until you get a while marble.  Every time you draw a black marble you put it back into the bucket and also add a new white marble to the bucket.  The random variable X denotes the total number of marbles you have drawn from the bucket. Find P(X = k) as a function of k. Compute E(X).

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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A bucket has three marbles.  Two are black and one is white.  You keep drawing until you get a while marble.  Every time you draw a black marble you put it back into the bucket and also add a new white marble to the bucket.  The random variable X denotes the total number of marbles you have drawn from the bucket.

  1. Find P(X = k) as a function of k.
  2. Compute E(X).  
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Step 1

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A bucket has 3 marbles

2 Black, 1 white

X denotes the total number of marbles drawn from the bucket

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