Let X 1 , X 2 , … , X m ∼ Geom ( p ) and they are IID. We want to find the probability P ( X 1 = x 1 , X 2 = x 2 , … , X m = x m | ∑ i = 1 m X i = t ) .

Question

Let       X    1    ,      X    2    ,  …  ,      X    m    ∼  Geom  (  p  ) and they are IID. We want to find the probability  P  (      X    1    =      x    1    ,      X    2    =      x    2    ,  …  ,      X    m    =      x    m          |          ∑          i      =      1        m        X    i    =  t  )  .

plomet6a · Accepted Answer

Step 1Based on my calculations   P      (          ∑              i        =        1            m              X      i        =    t    )    =      p    m    (  1  −  p      )          t      +      1        ⋅  (  t  +  m  )  ⋅                    (                            t        +        m        −        1                    m        −        1                            )            Step 2  P  (      X    1    =      x    1    ,      X    2    =      x    2    ,  …  ,      X    m    =      x    m    )  =  (  1  −  p      )          t            p    m

Let X_1, X_2,…,X_m∼Geom(p) and they are IID. We want to find the probability P(X_1=x_1, X_2=x_2, …, X_m=x_m|sum_{i=1}^{m} X_i=t).

Answered question

Answer & Explanation

New Questions in High school geometry