I have a brother 2 years older than I and we want to know if we share the same father. Both parents are deceased and we live in different states.

You can get a kinship test. You and the siblings would need to be tested. There are some on the market that can do kinship and "ethnicity" testing at the same time. I air quote ethnicity because it's really a population finder that looks for genetically similar groups in relation to deep geography, which isn't exactly the same thing as ethnicity (one's own culture). However, the test will show how closely you are related, it won't really prove who the father is. I personally would be cautious about presuming for sure without having the suspected father tested.

A note of caution, DNA tests can often be hard to inerpret and the results aren't always presented in a way that is easy to understand. What the test can and cannot tell you can be very confusing. Kinship tests can also be the most expensive . Read the FAQs and make sure you understand exactly what you're getting.

https://customercare.23andme.com/entries/21734308-Can-the-23andMe-Personal-Genome-Service-tell-me-if-my-sibling-and-I-are-half-or-full-siblings-


From familytreedna Family Finder (not recommended since you share a parent, it won't tell you anything. Providing link just for comparison of FAQs)
https://www.familytreedna.com/products.aspx


Two that specialize in kinship testing only:
Worldwide Genetics DNA Kinship and Family Relationship Testing (http://www.worldwidepaternity.com/dna-kinship.html)

https://www.orchidcellmark.com/kinship.html


Sincerely,
Rihanna (:

Can I ask why this is important to you? With both parents deceased, its not about inheritance so what's the big deal?