一道题目中两个变量是相互的，都可以是自变量或因变量，但我不知道如何判断哪个量为自变量，哪个量为因变
\u53d8\u91cf \u81ea\u53d8\u91cf \u56e0\u53d8\u91cf\u662f\u4ec0\u4e48\u5728\u6570\u5b66\u4e2d\uff0cy=f\uff08x\uff09\u3002\u5728\u8fd9\u4e00\u65b9\u7a0b\u4e2d\u81ea\u53d8\u91cf\u662fx\uff0c\u56e0\u53d8\u91cf\u662fy
\u4efb\u4f55\u4e00\u4e2a\u7cfb\u7edf\uff08\u6216\u6a21\u578b\uff09\u90fd\u662f\u7531\u5404\u79cd\u53d8\u91cf\u6784\u6210\u7684\uff0c\u5f53\u6211\u4eec\u5206\u6790\u8fd9\u4e9b\u7cfb\u7edf\uff08\u6216\u6a21\u578b\uff09\u65f6\uff0c\u53ef\u4ee5\u9009\u62e9\u7814\u7a76\u5176\u4e2d\u4e00\u4e9b\u53d8\u91cf\u5bf9\u53e6\u4e00\u4e9b\u53d8\u91cf\u7684\u5f71\u54cd\uff0c\u90a3\u4e48\u6211\u4eec\u9009\u62e9\u7684\u8fd9\u4e9b\u53d8\u91cf\u5c31\u79f0\u4e3a\u81ea\u53d8\u91cf\uff0c\u800c\u88ab\u5f71\u54cd\u7684\u91cf\u5c31\u88ab\u79f0\u4e3a\u56e0\u53d8\u91cf\u3002
\u81ea\u53d8\u91cf\u662f\u88ab\u64cd\u7eb5\u7684\u53d8\u91cf\uff0c\u800c\u56e0\u53d8\u91cf\u662f\u88ab\u6d4b\u5b9a\u6216\u88ab\u8bb0\u5f55\u7684\u53d8\u91cf\u3002\u8fd9\u4e24\u4e2a\u4e13\u4e1a\u7528\u8bed\u7684\u533a\u522b\u770b\u4e0a\u53bb\u4f1a\u4f7f\u5f88\u591a\u8bfb\u8005\u4ea7\u751f\u6df7\u6dc6\uff0c\u6b63\u5982\u4e00\u4e9b\u8bfb\u8005\u6240\u8bf4\u7684\u2014\u2014\u201c\u5168\u90e8\u53d8\u91cf\u90fd\u5177\u6709\u4f9d\u8d56\u6027\u201d\u3002\u4e0d\u8fc7\uff0c\u4e00\u65e6\u4f60\u8ba4\u8bc6\u5230\u8fd9\u79cd\u533a\u522b\uff0c\u5c31\u4f1a\u53d1\u73b0\u8fd9\u4e2a\u533a\u522b\u662f\u5fc5\u4e0d\u53ef\u5c11\u7684\u3002\u81ea\u53d8\u91cf\u4e0e\u56e0\u53d8\u91cf\u4e00\u8bcd\u4e3b\u8981\u7528\u4e8e\u53d8\u91cf\u88ab\u64cd\u7eb5\u7684\u5b9e\u9a8c\u7814\u7a76\u4e2d\uff0c\u5728\u8fd9\u79cd\u610f\u4e49\u4e0a\uff0c\u81ea\u53d8\u91cf\u5728\u7814\u7a76\u5bf9\u8c61\u53cd\u5e94\u5f62\u5f0f\u3001\u7279\u5f81\u3001\u76ee\u7684\u4e0a\u662f\u72ec\u7acb\u7684\uff0c\u5176\u4ed6\u4e00\u4e9b\u53d8\u91cf\u5219\u201c\u4f9d\u8d56\u4e8e\u201d\u64cd\u7eb5\u53d8\u91cf\u6216\u5b9e\u9a8c\u6761\u4ef6\u7684\u6539\u53d8\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u4ed6\u4eec\u662f\u5bf9\u201c\u5bf9\u8c61\u5c06\u505a\u4ec0\u4e48\u201d\u7684\u53cd\u5e94\u3002\u4e0e\u8fd9\u5b9a\u4e49\u7684\u672c\u8d28\u6709\u6240\u51b2\u7a81\uff0c\u8fd9\u4e2a\u8bcd\u4e5f\u7528\u4e8e\u6211\u4eec\u5c06\u89c2\u5bdf\u5bf9\u8c61\u6309\u7167\u5bf9\u8c61\u539f\u6709\u7684\u5c5e\u6027\u5206\u5230\u5404\u201c\u5b9e\u9a8c\u7ec4\u201d\u4e2d\uff0c\u800c\u4e0d\u662f\u64cd\u7eb5\u81ea\u53d8\u91cf\u7684\u7814\u7a76\u4e2d\u3002\u5982\u5728\u6bd4\u8f83\u7537\u5973\u6027\u767d\u7ec6\u80de\u6570\u7684\u5b9e\u9a8c\u4e2d\uff0c\u6027\u522b\u88ab\u79f0\u4e3a\u4e86\u81ea\u53d8\u91cf\uff0c\u800c\u767d\u7ec6\u80de\u6570\u5219\u4e3a\u56e0\u53d8\u91cf\u3002
\u6211\u77e5\u9053\u76f8\u5173\u5206\u6790\u4e0d\u7528
\u76f8\u5173\u5206\u6790\u662f\u5206\u6790\u4e24\u7ec4\u6570\u4e4b\u95f4\u7684\u76f8\u5173\u5173\u7cfb\uff0c\u4e0d\u9700\u8981\u786e\u5b9a\u81ea\u53d8\u91cf\u548c\u56e0\u53d8\u91cf
\u6240\u4ee5 \u9898\u4e2d\u6240\u8ff0\u9519\u8bef
绛旓細杩欎釜鏄牴鎹叿浣棰樼洰鑰屽畾鐨勶紝鏈绠鍗曠殑灏辨槸浣犵湅涓涓嬪厛鍝釜閲忓彉鍖栵紝鐒跺悗涓や竴涓啀璺熺潃鍙樺寲銆傚厛鍙樺寲鐨勫摢涓氨鏄嚜鍙橀噺銆
绛旓細鐢棰樼洰涓鍙互鐪嬪埌锛歑涓嶻鐨勭浉鍏崇郴鏁跋=0锛堟嫭鍙峰唴绗簲椤硅〃绀合侊級鑰屽浜庝簩缁存鎬佸垎甯冩湁涓绉嶉噸瑕佺殑缁撹灏辨槸锛涓や釜姝ｆ佸垎甯冮殢鏈鍙橀噺X涓嶻鐩镐簰鐙珛鐨勫厖鍒嗗繀瑕佹潯浠舵槸瀹冧滑鐨勭浉鍏崇郴鏁跋=0 鎵浠ュ彲鐭ワ細杩欎釜棰樼洰涓殑X涓嶻鏄浉浜鐙珛鐨勶紝骞朵笖X锛孻閮藉垎鍒湇浠庝竴缁存鎬佸垎甯 鏈夛細f(x,y)=1/(2蟺蟽1蟽2)*e^{-...
绛旓細鏄竴涓鐜囩殑棰橈細鍏堟敞鎰棰樼洰缁欑殑鏉′欢锛歺銆亂鏄嫭绔嬬殑 骞朵笖鏈夊悇鑷殑鍒嗗竷鍑芥暟 閭ｄ箞锛氭眰鍑猴細x銆亂鐨勮仈鍚堟鐜囧瘑搴 f锛坸锛寉锛=f锛坸锛塮锛坹锛夌劧鍚 鎸夌収瀹氫箟锛氬彟锛歓=X+Y F锛坺锛=P 锝沍銆妟锝=P锝沊+Y 銆坺锝 鐒跺悗鍒嗘儏鍐佃璁
绛旓細P(Z=0)=P(X=0){P(Y=0)+P(Y=-1)}=0.3 P(Z=1)=1-P(Z=0)=0.7 濡傛湁鎰忚锛屾杩庤璁猴紝鍏卞悓瀛︿範锛涘鏈夊府鍔╋紝璇烽変负婊℃剰鍥炵瓟锛
绛旓細P(Z=0)=P(X=0){P(Y=0)+P(Y=-1)}=0.3 P(Z=1)=1-P(Z=0)=0.7 濡傛湁鎰忚锛屾杩庤璁猴紝鍏卞悓瀛︿範锛涘鏈夊府鍔╋紝璇烽変负婊℃剰鍥炵瓟锛
绛旓細鍙互涓鸿礋)鍒橣椹-F=am 鑰岄殢鐫a瀛樺湪浣垮緱v=v0+at涔熷湪鍙樺寲 浣垮緱F涔熻窡闅弙鍙樺寲,鏁呰屽簲鍒椾唬鏁伴」,鍚屾浠ｅ叆 杩欐牱鏈缁堝舰鎴怓椹卞湪宸﹁竟,鍏朵粬閮藉湪鍙宠竟鐨勫彉閲忓舰寮,鍥鍙橀噺閮褰掔撼鍒皌鍘讳簡,闄ら潪浣犵殑棰樼洰涓嶆槸璁捐棰,鑰屾槸浠呯煡閬撳嚑涓潯浠,瑕佹眰璁＄畻鑰屽凡,閭ｄ箞璇风粰鍑哄叿浣撻鐩惂,浠栦滑蹇呯劧鏈夊綊绾虫硶鐨 ...
绛旓細涓嶄竴瀹氱殑锛屼綘鐨勯偅涓棰樼洰鎴戝府浣犵悊鐞嗘濊矾锛氾紙1锛塜鏄鎬佹讳綋锛屾墍浠1銆乆2鐩镐簰鐙珛锛岃鏈笂鏈夊畾鐞嗭紙杩欎釜缁撹寰堟槑鏄撅級锛氱浉浜掔嫭绔嬬殑涓や釜涓缁存鎬侀殢鏈鍙橀噺锛屾槸鍙互褰㈡垚浜岀淮姝ｆ侀殢鏈哄彉閲忕殑锛涳紙2锛(X1锛孹2)鏄簩缁存鎬侀殢鏈哄彉閲忎簡锛屽悗闈㈤兘鍙互涓茶捣鏉ヤ簡锛
绛旓細鍥鍙橀噺锛坉ependent variable锛夋槸鎸囧嚱鏁涓鐨勪笓涓氬悕璇嶏紝鍑芥暟鍏崇郴寮忎腑锛屾煇浜涚壒瀹氱殑鏁颁細闅忓彟涓涓紙鎴栧彟鍑犱釜锛変細鍙樺姩鐨勬暟鐨勫彉鍔ㄨ屽彉鍔ㄣ傚锛歒=f(X)锛屾寮忚〃绀轰负锛歒闅廥鐨勫彉鍖栬屽彉鍖栵紝Y鏄洜鍙橀噺锛孹鏄嚜鍙橀噺銆傚浜庡嚱鏁颁腑鐨勮嚜鍙橀噺鍜屽洜鍙橀噺鏈夋椂鏄浉浜掔殑锛鍗冲彉鍖栫殑閲忕殑鑷彉閲忥紝鐢卞彉鍖栫殑閲忚屽紩璧风殑鍙︿竴涓...
绛旓細鐩稿悓銆傚鍚岃仈绔嬬殑涓や釜浜屽厓涓娆℃柟绋嬬粍銆
绛旓細涓鑸柟娉曟槸鎶撲綇鍙樺寲涓殑鈥滀笉鍙橀噺鈥,浠ヤ笉鍙樺簲涓囧彉,棣栧厛鏍规嵁棰樻剰鐞嗘竻棰樼洰涓袱涓彉閲X銆乊鐨勫彉鍖栨儏鍐靛苟鎵惧嚭鐩稿叧甯搁噺,绗簩,鎸夌収鍥惧舰涓殑鍑犱綍鎬ц川鍙鐩镐簰鍏崇郴,鎵惧嚭涓涓熀鏈叧绯诲紡,鎶婄浉鍏崇殑閲忕敤涓涓嚜鍙橀噺鐨勮〃杈惧紡琛ㄨ揪鍑烘潵,鐒跺悗鍐嶆牴鎹鐩殑瑕佹眰,渚濇嵁鍑犱綍銆佷唬鏁扮煡璇嗚В鍑恒傜涓,纭畾鑷彉閲忕殑鍙栧艰寖鍥,鐢诲嚭鐩稿簲鐨勫浘璞°
