# statistics

Essay by chloe1124A, November 2014

Keywords

Continuous random variable

measured (not counted)

takes any value within a given interval

ä¸ä¸ªéæºåéå¨å¶åºé´åå½è½å¤åä»»ä½æ°å¼æ¶æå·æçåå¸ã

Continuous Probability Distribution

The distribution of a continuous random variable

No gaps within the interval

Normal Distribution

Bell-shaped

Symmetrical

Mean=median=mode

Location is determined by the mean, Î¼

Î¼å³å®æ­£ææ²çº¿çä¸­å¿ä½ç½®

uåæ¢ï¼ä¸ºäºä¾¿äºæè¿°ååºç¨ï¼å¸¸å°æ­£æåéä½æ°æ®è½¬æ¢ãÎ¼æ¯æ­£æåå¸çä½ç½®åæ°ï¼æè¿°æ­£æåå¸çéä¸­è¶å¿ä½ç½®ãæ­£æåå¸ä»¥X=Î¼ä¸ºå¯¹ç§°è½´ï¼å·¦å³å®å¨å¯¹ç§°ãæ­£æåå¸çåæ°ãä¸­ä½æ°ãä¼æ°ç¸åï¼åç­äºÎ¼ã

Spread is determined by the standard deviation, Ï

æ åå·®Ïå³å®æ­£ææ²çº¿çé¡å³­ææå¹³ç¨åº¦ãÏè¶å°ï¼æ²çº¿è¶é¡å³­ï¼Ïè¶å¤§ï¼æ²çº¿è¶æå¹³ã

Ïæè¿°æ­£æåå¸èµææ°æ®åå¸çç¦»æ£ç¨åº¦ï¼Ïè¶å¤§ï¼æ°æ®åå¸è¶åæ£ï¼Ïè¶å°ï¼æ°æ®åå¸è¶éä¸­ãä¹ç§°ä¸ºæ¯æ­£æåå¸çå½¢ç¶åæ°ï¼Ïè¶å¤§ï¼æ²çº¿è¶æå¹³ï¼åä¹ï¼Ïè¶å°ï¼æ²çº¿è¶ç¦é«ã

The random variable has an infinite theoretical range:

to +

The formula for the normal probability density function:

Where

X = any value of the continuous variable

Î¼ = the population mean

Ï = the population standard deviation

e = the mathematical constant approximated by 2.71828

Ï = the mathematical constant approximated by 3.14159

æ­£æåå¸åæ­£å¤ªæ²çº¿

å¦ææ»ä½å¯åº¦æ²çº¿æ¯æèè¿ä¼¼æ¯å½æ°

çå¾åï¼å¶ä¸­åå«è¡¨ç¤ºæ»ä½çå¹³åæ°ï¼åæ åå·®ï¼è¿ä¸ªæ»ä½æ¯ææ éå®¹éçæ½è±¡æ»ä½ï¼å¶åå¸å«ä½æ­£å¤ªåå¸ï¼è®°ä½Nï¼ï¼

å½æ¶ï¼å½æ°

å¯¹åºçæ»ä½ç§°ä¸ºæ åæ­£å¤ªæ»ä½ï¼è®°ä½N(0,1)

Ïæè¿°æ­£æåå¸èµææ°æ®åå¸çç¦»æ£ç¨åº¦ï¼Ïè¶å¤§ï¼æ°æ®åå¸è¶åæ£ï¼Ïè¶å°ï¼æ°æ®åå¸è¶éä¸­ãä¹ç§°ä¸ºæ¯æ­£æåå¸çå½¢ç¶åæ°ï¼Ïè¶å¤§ï¼æ²çº¿è¶æå¹³ï¼åä¹ï¼Ïè¶å°ï¼æ²çº¿è¶ç¦é«ã

æ åæ­£å¤ªåå¸è¡¨

ï¼X0ï¼ï¼P(X<XO) è¡¨ç¤ºæ»ä½åå¼å°äºx0çæ¦ç

ä¸æ ¹æ®å¯¹ç§°æ§å¯å¾

ï¼X0ï¼ï¼1-ï¼ï¼X0ï¼

A normal distribution with

a mean of zero, and

a standard deviation of one

ä¸è¬æ­£å¤ªæ»ä½Nï¼ ï¼ ï¼åä¸ºæ åæ­£å¤ªæ»ä½Nï¼ 0 ï¼1 ï¼