The number of Bernoulli trials required to produce exactly 1 success and at least 1 failure.Let X be the number of Bernoulli (p) trials required to produce exactly 1 success and at least 1 failure. Find the distribution of X.How can I answer this question if I don't know how many trials have taken place?For context, the section this comes from was about Poisson distribution. ( n k ) p k ( 1 − p ) ( n − k ) → e − μ μ k k ! as n → ∞ and p → 0 with n p = μHowever I read in a different book that you can use the Geometric probability model for Bernoulli trials: Geom(p) P ( X = x ) = q X − 1 Pwhere p is prob. of success, X is number of trials, and q is prob. of failure

Question

The number of Bernoulli trials required to produce exactly 1 success and at least 1 failure.Let X be the number of Bernoulli (p) trials required to produce exactly 1 success and at least 1 failure. Find the distribution of X.How can I answer this question if I don&#039;t know how many trials have taken place?For context, the section this comes from was about Poisson distribution.                    (                    n      k                      )                  p    k    (  1  −  p      )          (      n      −      k      )        →                    e                  −          μ                            μ                  k                            k      !        as   n  →  ∞   and   p  →  0   with   n  p  =  μHowever I read in a different book that you can use the Geometric probability model for Bernoulli trials: Geom(p)  P  (  X  =  x  )  =      q          X      −      1        Pwhere p is prob. of success, X is number of trials, and q is prob. of failure

nedervdq3 · Accepted Answer

Step 1The only posibilities for X ( since exactly one sucess is allowed)  x  =  2  −  −  &amp;gt;  {  S  F  ,  F  S  }    x  =  3  −  −  &amp;gt;  {  F  F  S  }    x  =  4  −  −  −  &amp;gt;  {  F  F  F  S  }Step 2If   p  =  P  (  S  )  P  (  X  =  2  )  =            2.      p      .      (      1      −      p      )              1      −              p                  2                      P  (  X  =  x  )  =            (      1      −      p              )        2            .      (      1      −      p              )                  x          −          2                    .      p              1      −              p        2              =            (      1      −      p              )                  x                    .      p              1      −              p        2                    ∀  x  ≥  3the denominator   1  −      p    2   is because you&#039;re not allowing the secuence SS

Let X be the number of Bernoulli (p) trials required to produce exactly 1 success and at least 1 failure. Find the distribution of X. How can I answer this question if I don't know how many trials have taken place?

Answered question

Answer & Explanation

New Questions in High school geometry