  Electrical quantum conductors coupled to microwave resonators have in the
last decade emerged as a versatile testbed for controllable light-matter
interaction on the nanometer scale. Recent experimental progress with high
impedance resonators has resulted in conductor-resonator systems with a large,
dimensionless coupling parameter $\lambda \gtrsim 0.1$, well beyond the small
coupling regime $\lambda \ll 1$. Motivated by this progress, we here analyse
theoretically the joint statistics of transported electrons and emitted photons
in a single level quantum dot coupled to a microwave resonator, for arbitrarily
large $\lambda$. Describing the electron-photon dynamics via a number-resolved
master equation, we evaluate the joint long-time probability distribution as
well as joint short-time, $g^{(2)}(t)$, correlation functions. Considering the
high-bias regime, with sequential electron tunneling and working in the damping
basis, allows us to obtain analytical results for both transport cumulants and
$g^{(2)}(t)$ functions. It is found that the photons emitted out of the
resonator are bunched and display a super-Poissonian statistics, for all system
parameters. However, the electron transport properties are found to be
unaffected by the coupling to the resonator, anti-bunched and with
sub-Poissonian statistics. From the joint distribution we identify regimes of
electron tunneling induced photon cascades and very large $g^{(2)}(t)$
functions. All $g^{(2)}(t)$-functions are found to be independent of $\lambda$.
We also identify conditions for and transport signatures of a thermal resonator
photon state.
