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Candidates for a certain job have to pass two screening stages. The probability of a candidate’s...

  1. Candidates for a certain job have to pass two screening stages. The probability of a candidate’s passing the first stage is 0.5. If a candidate passes the first stage, he/she has a probability of passing the second stage and getting the job. In a certain year there were 3 candidates for the job. Denote by X the number of candidates who pass the first stage, and Y the number of candidates who pass the second stage. a) Develop the joint probability distribution between X and Y.
Math   Statistics-And-Probability   
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Answer #1

The number of candidates who pass the first stage out of 3 had Binomial distribution with PMF,

Let the probability that a first stage qualified candidate passes the second stage be . The the conditional PMF,

The joint  probability distribution between X and Y is

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