NOVELTY - A fluorine-containing random copolymer contains (in mol%) ethylene-group containing structural unit (10-75), fluoroalkyl perfluoro vinyl ether (4-70) (1), hydroxyl-group containing unsaturated monomer (10-70) and polysiloxane compound (0.001-10) (2,3,4,5,6,7 and 8). The fluorine-containing random copolymer has weight average molecular weight of 5000-300000 measured by gel permeation chromatography with respect to polystyrene conversion and molecular weight distribution of 1-5.    USE - Fluorine-containing random copolymer used for producing double bond containing fluorine-containing random copolymer for coating-material composition, varnish, coating material, coating film (all claimed), optical medium, anti-reflective film, sheath material, optical fiber, protective film, glass filers, solar cell and semiconductor material.    ADVANTAGE - The fluorine-containing random copolymer has excellent solubility with respect to organic solvent and double bond containing fluorine-containing random copolymer and shelf life. The coated film containing fluorine-containing random copolymer has excellent low-refractive-index property, transparency, stain resistance, water-repellent oil repellency, surface lubricacy and abrasion resistance.    DETAILED DESCRIPTION - A fluorine-containing random copolymer contains (in mol%) ethylene-group containing structural unit (10-75), fluoroalkyl perfluoro vinyl ether (4-70) of formula (1), hydroxyl-group containing unsaturated monomer (10-70) and polysiloxane compound (0.001-10) of formulae (2,3,4,5,6,7 and 8). The fluorine-containing random copolymer has weight average molecular weight of 5000-300000 measured by gel permeation chromatography with respect to polystyrene conversion and molecular weight distribution of 1-5. The ethylene-group containing structural unit is of formula: -(C(-R1)(-R2)-C(-R3)(-R4))-. The hydroxyl-group containing unsaturated monomer is of formula: -(CH2-CH(-(CH2)p-O-R6-OH))-.    R1-R4=H, fluorine or trifluoromethyl, preferably fluorine;    R5=1-30C perfluoroalkyl or fluorine-containing alkyl;    R6=1-10C alkylene;    R7=H or methyl;    R8,R9=H, 1-4C alkyl, phenyl, cyclohexyl, -CF3, -CH2CF3, -(CH2)2CF3, -(CH2)3CF3 or -C(CH3)3;    R10=H or 1-6C alkyl;    X,Y',Z=H or fluorine;    p=0-6;    n=1-420;    r=1-6;    m,q=1-210;and    k=1-6.    when X is H, Z and/or Y' is fluorine. An INDEPENDENT CLAIM is included for manufacture of fluorine-containing random copolymer, which involves copolymerizing a polymerization component by solution-polymerizing method using solvent chosen from ethyl acetate, butyl acetate, xylene, toluene, methyl ethyl ketone and/or methyl isobutyl ketone.