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

Diego Barr

Diego Barr

Answered question

2022-10-15

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

Answer & Explanation

spornya1

spornya1

Beginner2022-10-16Added 18 answers

Step 1
If 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.

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