随机变量概率密度函数的性质

米博体育дёү.иҝһз»ӯеһӢйҡҸжңәеҸҳйҮҸ1.е®ҡд№үеҰӮжһңйҡҸжңәеҸҳйҮҸXзҡ„еҲҶеёғеҮҪж•°F(x)еҸҜд»ҘиЎЁзӨәжҲҗжҹҗдёҖйқһиҙҹеҮҪж•°f(x)зҡ„з§ҜеҲҶF(x)=вҲһ<x<вҲһ,еҲҷз§°Xдёәиҝһз»ӯеһӢйҡҸжңәеҸҳйҮҸ,е…¶дёӯf(x)з§°дёәXзҡ„жҰӮзҺҮеҜҶеәҰ米博体育:随机变量概率密度函数的性质(йҡҸжңәеҸҳйҮҸеҮҪж•°зҡ„еҜҶеәҰеҮҪж•°)е®ҡд№ү:жҰӮзҺҮеҜҶеәҰеҮҪж•°f(x)зӯүдәҺ(жҰӮзҺҮ/еҢәй—ҙй•ҝеәҰеҲҶеёғеҮҪж•°F(X)жұӮеҜјеҗҺзӯүдәҺf(x)жҖ§иҙЁ1)йқһиҙҹжҖ§(2)规иҢғжҖ§(34)3гҖҒеқҮеҢҖеҲҶеёғе®ҡд№ү:иӢҘиҝһз»ӯеһӢйҡҸжңәеҸҳйҮҸXе…·жңүжҰӮзҺҮеҜҶ

2.жҰӮзҺҮеҜҶеәҰеҮҪж•°жҖ§иҙЁеүҚдёӨжқЎжҖ§иҙЁдёәе……еҲҶеҝ…иҰҒжқЎд»¶жҖ§иҙЁ2еҰӮеӣҫ:жҖ§иҙЁ2еёёз”ЁдәҺжұӮеҸӮж•°жҖ§иҙЁ3еҰӮеӣҫеҜ№дәҺиҝһз»ӯжҖ§йҡҸжңәеҸҳйҮҸ,жҲ‘们дёҚе…іеҝғеңЁжҹҗдёҖзӮ№зҡ„еҸ–еҖј,иҖҢеңЁд№ҺеңЁжҹҗдёҖеҢәй—ҙдёҠеҸ–еҖјзҡ„й—®йўҳгҖӮиҝһз»ӯжҖ§йҡҸжңә

д»ҠеӨ米博体育©жҲ‘е°ұи®Іи®Іеә”иҜҘеҰӮдҪ•зҗҶи§ЈжҰӮзҺҮеҲҶеёғеҮҪж•°е’ҢжҰӮзҺҮеҜҶеәҰеҮҪж•°зҡ„й—®йўҳгҖӮжҳҜдёҚжҳҜд№ҚдёҖзңӢзү№еҲ«еғҸ,е®№жҳ“иҝ·зіҠгҖӮеҰӮжһңдҪж„ҹеҲ°иҝ·зіҠ,жҒӯе–ңдҪжүҫеҲ°жҲ‘еҪ“е№ҙзҡ„ж„ҹи§үдәҶгҖӮе…Ҳд»ҺзҰ»ж•ЈеһӢйҡҸжңәеҸҳйҮҸе’Ңиҝһз»ӯжҖ§йҡҸжңәеҸҳйҮҸиҜҙиө·

йҡҸжңәеҸҳйҮҸеҮҪж•°зҡ„еҜҶеәҰеҮҪж•°

йҡҸжңәеҸҳйҮҸдёҺеҲҶеёғеҮҪж•°жҳҜдёҖдёҖеҜ№еә”зҡ„пјҢиҖҢжүҖи°“йҡҸжңәеҸҳйҮҸXзҡ„еҲҶеёғеҮҪж•°пјҢжҢҮзҡ„жҳҜFX(x=P(XвүӨxвҲҖxвҲҲR.е®№жҳ“йӘҢиҜҒFX(x)ж»Ўи¶іеҲҶеёғеҮҪж•°зҡ„е®ҡд№үгҖӮдәҢгҖҒиҝһз»ӯжҖ§йҡҸжңәеҸҳйҮҸгҖҒжҰӮзҺҮеҜҶ

вҖӢдёәиҝһз»ӯйҡҸжңәеҸҳйҮҸ,вҖӢз§°дёәвҖӢзҡ„жҰӮзҺҮеҜҶеәҰеҮҪж•°,з®Җз§°жҰӮзҺҮеҜҶеәҰжҲ–еҜҶеәҰеҮҪж•°гҖӮжҰӮзҺҮеҜҶеәҰеҮҪж•°е…·жңүеҰӮдёӢжҖ§иҙЁ1)йқһиҙҹжҖ§:вҖӢ(2)规иҢғжҖ§:вҖӢжқЎд»¶жҰӮзҺҮеҜҶеәҰеҮҪж•°:еҜ№дәҺд»»ж„Ҹз»ҷе®ҡзҡ„вҖӢ,еңЁз»ҷе®ҡеҢәй—ҙ

еҜ№жғ…еҶө1,еҸҜд»Ҙе°ҶxеҶҷдёәx=cc-xеҜ№жғ…еҶө2,еҸҜд»Ҙе°ҶxеҶҷдёәx=cx-cе…¶дёӯеёёж•°йЎ№з§ҜеҲҶз»“жһңдёәc,иҖҢеҗҺйқўдёӨйЎ№еҖҹеҠ©жҖ§иҙЁf(x-c)=f(x+c)зӣёдә’жҠөж¶Ҳдёә0,жүҖд»ҘEX=c.з»“жһңдёҖйўҳзӣ®йҡҸжңәеҸҳйҮҸxзҡ„жҰӮзҺҮеҜҶ

жң¬ж–Үз«е°Ҷд»Ӣз»ҚеңЁиҖғз”иҢғеӣҙеҶ…зҡ„еёёи§Ғзҡ„еҲҶеёғзҡ„жҰӮзҺҮеҜҶеәҰеҮҪж•°,еҲҶеёғеҮҪж•°,жңҹжңӣ,ж–№е·®.иҖғз”жҰӮзҺҮи®әиҖғеҜҹзҡ„еҲҶеёғе°ҶдёҚдјҡи¶…еҮәжӯӨиҢғеӣҙ.зҰ»ж•ЈеһӢйҡҸжңәеҸҳйҮҸ1.0⑴еҲҶеёғXвҲјB(1,p

иҝҷйҮҢf(x)е°ұжҳҜжҲ‘们жүҖиҜҙзҡ„жҰӮзҺҮеҜҶеәҰеҮҪж•°пјҢйҮҚзӮ№жҳҜвҡпёҸжҲ‘们дёҖзӣҙжүҖиҜҙзҡ„жҰӮзҺҮеҜҶеәҰеҮҪж•°е°ұжҳҜеҸӘжҲ‘们жғіиҰҒжұӮйқўз§Ҝ米博体育:随机变量概率密度函数的性质(йҡҸжңәеҸҳйҮҸеҮҪж•°зҡ„еҜҶеәҰеҮҪж•°)и§Јзӯ米博体育”пјҡи§ЈпјҡZ=2X-Yзҡ„еҲҶеёғеҮҪж•°дёәпјҡFZпјҲzпјү=P{ZвүӨz}пјҢеҪ“zвүӨ0ж—¶пјҢFZпјҲzпјү=0пјҢеҪ“0пјңzпјң1ж—¶пјҢz=2x-yдёҺxиҪҙзҡ„дәӨзӮ№дёәпјҡ(z2пјҢ0)пјҢдёҺx=1зҡ„дәӨзӮ№дёәпјҲ1пјҢ2-zпјүпјҢF