For both PAL and NTSC and Rec 601 digital:
Y= 0.299R + 0.589G + 0.114B
For HD they changed the coeffts slightly.
https://en.wikipedia.org/wiki/Rec._709 This was a somewhat controversial decision. It gave a larger colour gamut but left an incompatibility.
For use with vintage monochrome sets it's not at all critical. You could even use the green signal on its own and get fairly good results.
There a lot more background to this. For one thing the RGB> YCbCr matrixing is specified on gamma corrected signals. This results in some Y travelling in colour difference and vice versa. This matters because the chroma channels have reduced bandwidth. The technical name for this is failure of constant luminance.
Some early colour cameras had a separate Y tube. For example the EMI 2001 and Marconi Mk VII. This reduced registration problems and gave better compatibility with monochrome receivers. Most later cameras were 3 tube but with "highs out of green". In other words all high frequency Y was taken from the green tube only.
Further reading on constant luminance:
http://downloads.bbc.co.uk/rd/pubs/reports/1972-29.pdf
https://books.google.co.uk/books?id=...nance.&f=false
http://www.bbc.co.uk/rd/publications/rdreport_1990_02