Proof of a formula with two geometric random variables

  • #1
2
0
Homework Statement:
If G_1 and G_2 are independent geometric random variables with parameters p_1 and p_2 respectively, show that
Relevant Equations:
P(G_1<G_2)=p_1(1-p_2)/(p_1+p_2-p_1p_2)
The image above is the problem and the image below is the solution I have tried but failed.

MVIMG_20210209_102231_recompress.jpg
1612521305080_recompress.jpg
 

Answers and Replies

  • #2
FactChecker
Science Advisor
Gold Member
6,270
2,437
You first equation is multiple-counting many cases. You should sum the cases where ##G_1 = k##, not ##G_1 \le k##
 
  • #3
2
0
You first equation is multiple-counting many cases. You should sum the cases where ##G_1 = k##, not ##G_1 \le k##
Get it, thank you very much!
 

Related Threads on Proof of a formula with two geometric random variables

Replies
1
Views
3K
Replies
4
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
0
Views
2K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
1
Views
4K
Replies
11
Views
2K
Replies
5
Views
4K
Top