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We present a study of the flux distribution of a sample of 15 Intermediate and Low-energy peaked blazars using XMM-Newton observations in a total of 57 epochs on short-term timescales. We characterise the X-ray variability of all of the light curves using excess fractional variability amplitude and found that only 24 light curves in 7 sources are significantly variable. In order to characterise the origin of X-ray variability in these blazars, we fit the flux distributions of all these light curves using Gaussian and lognormal distributions, as any non-Gaussian perturbation could indicate the imprints of fluctuations in the accretion disc, which could be Doppler boosted through the relativistic jets in blazars. However, intra-day variability, as seen in our observations, is difficult to reconcile using disc components as the emissions in such sources are mostly dominated by jets. We used Anderson–Darling (AD) and χ 2 tests to fit the histograms. In 11 observations of 4 blazars, namely, ON 231, 3C 273, PKS 0235+164 and PKS 0521-365, both models equally fit the flux distributions. In the rest of the observations, we are unable to model them with any distribution. In two sources, namely, BL Lacertae and S4 0954+650, the lognormal distribution is preferred over the normal distribution, which could arise from non-Gaussian perturbations from relativistic jets or linear Gaussian perturbation in the particle time scale leading to such flux distributions. [ABSTRACT FROM AUTHOR]