Please tell me, why low-pass FIR Equiripple filters are designed with 3 dB of ripple in the pass-band and at least 60 dB of attenuation in the stop-band and not other values ? I want to know are these values simply a convention?
Stop band attenuation is a good thing right? After all it's the primary reason why you want a frequency selective filter: stop the unwanted frequencies. So a 60dB attenuation in the stop band of a filter is considered to be the norm in many typical applications. But not always so, as the comments indicate; you must always refer to your application requirements for determining how much attenuation is enough (or necessary) for your case.
That being said, there exist tradeoffs in filter design, just like in many other design procedures. And the most fundamental of those tradeoff parameters, for digital FIR filter design, are namely the passband ripple, stopband attenuation, transition band width and the resulting filter's length.
Among these parameters transition band width and stop band attenuation affects the selectivity quality of your filter. But a short transition band with a large stop band attenuation means a (very) high order (long impulse response) FIR filter, which creates opposition due to computational burden.
To overcome this computational burden, due to narrow transition band, once can consider relaxing the filter's definition in, for example, the pass-band region, so that instead of a monotonic or an un-equal ripple filter, you distribute the ripples equally by allowing as large as possible but fixed amplitude ripples in every where through the passband, so that the FIR filter length will be kept short enough.
3dB passband ripple can be considered a reasonable choice for some applications in which pass band distortions due to those ripples may be tolerable.