Let X_i, i=1,…,n be Geometric i.i.d random variables, which represent the number of fails, with parameter p.

Hayley Bernard 2022-07-15 Answered
How to find a probability that sum of geometric variables is less than a number
Let X i , i = 1 , , n be Geometric i.i.d random variables, which represent the number of fails, with parameter p.
Calculate or estimate from above and below:
P ( i = 1 n X i A ) , A N .
I know that sum of the geometric random variables is the negative binomial, but I would not know all the parameters for the negative binomial r.v.
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Answers (1)

kuglatid4
Answered 2022-07-16 Author has 12 answers
Step 1
You probably mean A N , i.e. A is a natural number. You should probably use CLT here, as n is large, Xi are iid with μ < , σ 2 <
P ( S n < A ) = P ( S n n μ σ n < A n μ σ n ) Φ ( z ).
Step 2
Here z = A n μ σ n , and μ , σ are mean and sd of each X i , which you can easily find.
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