A method of determining, in a sample from a female subject pregnant with a fetus, a portion of RNA that is of fetal origin, the method comprising: receiving a plurality of sequence reads, wherein the sequence reads are obtained from an analysis of RNA molecules obtained from the sample, the sample containing a mixture of maternal- and fetal-derived RNA molecules; identifying, by a computer system, locations of the sequence reads in a reference sequence; identifying one or more informative maternal loci, each of which is homozygous in the fetus for a corresponding first allele and which is heterozygous in the pregnant female subject for the corresponding first allele and a corresponding second allele; filtering the one or more informative maternal loci to identify one or more filtered informative maternal loci: that are located within an expressed region of the reference sequence, at which at least a first predetermined number of sequence reads in the plurality of sequence reads containing the corresponding first allele are located, and at which at least a second predetermined number of sequence reads in the plurality of sequence reads containing the corresponding second allele are located, for each of the filtered informative maternal loci: determining a first number of sequence reads located at the filtered informative maternal locus and containing the corresponding first allele, determining a second number of sequence reads located at the filtered informative maternal locus and containing the corresponding second allele, calculating a sum of the first number and the second number, calculating a maternal ratio of the second number divided by the sum, determining a scalar representing a total expression at the filtered informative maternal locus relative to expression of the corresponding second allele in the pregnant female subject, multiplying the maternal ratio by the scalar to obtain a maternal contribution, calculating a fetal contribution as one minus the maternal contribution, and determining a portion of RNA in the sample that is of fetal origin, wherein the portion is an average of the fetal contributions for the filtered informative maternal loci. receiving a plurality of sequence reads, wherein the sequence reads are obtained from an analysis of RNA molecules obtained from the sample, the sample containing a mixture of maternal- and fetal-derived RNA molecules; identifying, by a computer system, locations of the sequence reads in a reference sequence; identifying one or more informative maternal loci, each of which is homozygous in the fetus for a corresponding first allele and which is heterozygous in the pregnant female subject for the corresponding first allele and a corresponding second allele; filtering the one or more informative maternal loci to identify one or more filtered informative maternal loci: that are located within an expressed region of the reference sequence, at which at least a first predetermined number of sequence reads in the plurality of sequence reads containing the corresponding first allele are located, and at which at least a second predetermined number of sequence reads in the plurality of sequence reads containing the corresponding second allele are located, that are located within an expressed region of the reference sequence, at which at least a first predetermined number of sequence reads in the plurality of sequence reads containing the corresponding first allele are located, and at which at least a second predetermined number of sequence reads in the plurality of sequence reads containing the corresponding second allele are located, for each of the filtered informative maternal loci: determining a first number of sequence reads located at the filtered informative maternal locus and containing the corresponding first allele, determining a second number of sequence reads located at the filtered informative maternal locus and containing the corresponding second allele, calculating a sum of the first number and the second number, calculating a maternal ratio of the second number divided by the sum, determining a scalar representing a total expression at the filtered informative maternal locus relative to expression of the corresponding second allele in the pregnant female subject, multiplying the maternal ratio by the scalar to obtain a maternal contribution, calculating a fetal contribution as one minus the maternal contribution, and determining a first number of sequence reads located at the filtered informative maternal locus and containing the corresponding first allele, determining a second number of sequence reads located at the filtered informative maternal locus and containing the corresponding second allele, calculating a sum of the first number and the second number, calculating a maternal ratio of the second number divided by the sum, determining a scalar representing a total expression at the filtered informative maternal locus relative to expression of the corresponding second allele in the pregnant female subject, multiplying the maternal ratio by the scalar to obtain a maternal contribution, calculating a fetal contribution as one minus the maternal contribution, and determining a portion of RNA in the sample that is of fetal origin, wherein the portion is an average of the fetal contributions for the filtered informative maternal loci.