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We present a determination of the distributions of photon spectral index andgamma-ray flux - the so called LogN-LogS relation - for the 352 blazarsdetected with a greater than approximately seven sigma detection threshold andlocated above +/- 20 degrees Galactic latitude by the Large Area Telescope ofthe Fermi Gamma-ray Space Telescope in its first year catalog. Because the fluxdetection threshold depends on the photon index, the observed raw distributionsdo not provide the true LogN-LogS counts or the true distribution of the photonindex. We use the non-parametric methods developed by Efron and Petrosian toreconstruct the intrinsic distributions from the observed ones which accountfor the data truncations introduced by observational bias and includes theeffects of the possible correlation between the two variables. We demonstratethe robustness of our procedures using a simulated data set of blazars and thenapply these to the real data and find that for the population as a whole theintrinsic flux distribution can be represented by a broken power law with highand low indexes of -2.37 +/- 0.13 and -1.70 +/- 0.26, respectively, and theintrinsic photon index distribution can be represented by a Gaussian with meanof 2.41 +/- 0.13 and width of 0.25 +/- 0.03. We also find the intrinsicdistributions for the sub-populations of BL Lac and FSRQs type blazarsseparately. We then calculate the contribution of Fermi blazars to the diffuseextragalactic gamma-ray background radiation. Under the assumption that theflux distribution of blazars continues to arbitrarily low fluxes, we calculatethe best fit contribution of all blazars to the total extragalactic gamma-rayoutput to be 60%, with a large uncertainty.

Flux and Photon Spectral Index Distributions of Fermi-LAT Blazars And Contribution To The Extragalactic Gamma-ray Background