Is the sum of two independent geometric random variables with the same success probability a geometric random variable?

Question

spornya1 · Accepted Answer

Step 1If X and Y are geometric random variables, they are each a count of Bernoulii trials until the first success.Z then counts Bernoulii trials until the second success.Step 2                              P          Z                (        z        )                            =                  ∑                      k            =            1                                z            −            1                                    P          X                (        k        )                  P          Y                (        z        −        k        )                              Note:                       k                     cannot be greater than                       z            −            1                                                            ⋮                                          =        (        z        −        1        )        (        1        −        p                  )                      z            −            2                                    p          2                    This is called a negative binomial distribution.

Is the sum of two independent geometric random variables with the same success probability parameter a geometric random variable? What is it's distribution?

Answered question

Answer & Explanation

New Questions in High school geometry