That it lasts a year fail on rst use note that if and

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Unformatted text preview: 1#'¢ ©§ 5 £ ¢ 8© A# ¡ U E©F¨¦¥'¢ §£ 8© 9&¥ ¡ @ Microchip lasts through first use , camera good ©§ 5 £ ¥ $1#'¢ Independence Does knowing that one event has occured alway have an impact on the probability of another event? ? DEFINITION: (Def. 3.9, p. 131) Events and are said to be independent if or get an even number “Not independent” = “DEPENDENT.” # greater than 3 Ex. Die Toss: ¥ and DEPENDENT, INDEPENDENT. §%7'¢…¨¦¥¤&© #£ § £ ¢ §¨¥ r7£'…§¨¦¥£¤&%$"¦¥'¢ 5 # ¢ ¢ ©§# 4 £ # ¥ and ¥ , and ) # greater than 2 # ¡ ( © 6§ ) "¦¤¢ 5fW g8 © ) "¥ ¡ 4 ¥£ 3 @ † c 4 †c © # 4 ( © § # 4 ¥ £ 2r"('¢ 4@ W g8 pr"¥ ¡ 3 £ © § #£  © § ¥£ (12© § ) '¢ ( F%1¤¢ & © ( F¨¦'¢ ¡  @ W † h † c † ` 8 @ © 8) A© 0¡  e@ W † h † g8 © @ c 8© A# ¡ e@ W † c † H 8 © @ 8© 9&¥ ¡  '§ %#"'¢ @ W † h † c † ` † H †  8 © B ¡ &( © $ £ and § £¢ ©§ 5 £ ¦¥¤&F26#'¦¥¤¢ § £¢ ©§ 5 £ ¨¦¥'&%6#¤¦¥¤¢ EXAMPLE : Toss a balanced die.  21#'&¨¥ r1#¤¢ § £¢ ©§ 5 £  NOTE: If chip does not fail during first year–It cannot fail  ¡ during the first year. Is camera good ©§ ¨ is  ©U  H ©§ £ EX` c &¦¥¤¢ £ '¢ If it lasts through its first use, prob. that it lasts a year ¥ ¦ fail on first use Note that if and are independent then [by Mult. Law] [by independence] 80 STA 2023 c B.Presnell & D.Wackerly - Lecture 6 STA 2023 c B.Presnell & D.Wackerly - Lecture 6 81 Ex. (LAST TIME!!!) Odds are 2:1 that when H and T This is another way to define independence: (p. 133) and winner of each recorded. Odds are 2:1 that H wins means H wins with prob. ` ¢iF§ ‚€1H£ ¢H H ©  )  3 WARNING . T wins with prob. `  21#'…¨¦¥¤&%# „¦¥'¢ § £ ¢§ £ ¢ © § 4 £ Independent play racquetball, H will win. H and T play 3 matches, . Probs. given Do NOT confuse INDEPENDENT with MUTUALLY in the example for 8 possible outcomes were c...
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