The Federal Bureau of Investigation (FBI), the National Aeronautics and Space Administration (NASA), and the Environmental Protection Agency (EPA) are

An agency within a cabinet department.

An Agency with in a capital department.

An Independent agency and a regulatory agency.

Explanation:

The FBI is the security security service and domestic intelligence agency of the USA. It is the principal law enforcement agency.

NASA stands for National Aeronautics Space Agency of the US federal government. It was founded in 1958 and it is responsible for aeronautics and aerospace research along with civilian space program.

EPA is abbreviated form of Environmental Protection Agency. It is an agency of US federal government, President Nixon proposed the establishment of EPA and it started functioning from December 1970. An agency within a cabinet department.