an urn contains n red and n blue balls. Balls are drawn at random (without replacement)...
an urn contains n red and n blue balls. Balls are drawn at random (without replacement) in stages until one color is depleted. The number of draws until this event happens is called waiting time. what is the distribution of this waiting time?
Homework Answers
The distribution of this waiting time can be a negative binomial distribution
Our waiting time is till n red or n blue balls are drawn , this can be termed as number of trials before nth success
Let X be the number of balls drawn before nth success that is nth red (say) drawn
p is the probability of drawing a red ball
Then probability distribution of X is
Let Y be the number of balls drawn before nth success that is nth blue drawn
p is the probability of drawing a blue ball
Then probability distribution of Y is
Probability distribution of waiting time for nth blue or red ball is
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