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S  0u ``  >*  0`{     * Copyright (c) 2004 Brooks/Cole, a division of Thomson Learning, Inc. >\Df B H  0޽h ? ̙33 Default Design" 00"(  0 0 0@`g DChapter 4 Continuous Random Variables and Probability Distributions *E0(2 0;<H 0 0޽h ? 3380___PPT10.^- @4-(  4 4 6 8c"`G =4.1 Continuous Random Variables and Probability Distributions(>0(20:<H 4 0޽h ? 3380___PPT10. Pۘx ( P (     0@ @0@ MContinuous Random Variables 2(  0 @r  kA random variable X is continuous if its set of possible values is an entire interval of numbers (If A < B, then any number x between A and B is possible). 2$$$ $D$$$$$$ $$$$$H  0޽h ? ̙33 `@(    0 P  JProbability Distribution 2(  0# `\  Let X be a continuous rv. Then a probability distribution or probability density function (pdf) of X is a function f (x) such that for any two numbers a and b, 2$$$>$$$$$$$ $$$$$,DB`  c $A ?? P    02  p  $The graph of f is the density curve.B% 2 $$$ $$H  0޽h ? ̙33 p8(  8 8 0< z TProbability Density Function0 2( 8 0@ p4 For f (x) to be a pdfH0 2$$$$$p 8 0G P`E p$D  0<4___PPT9  f (x) > 0 for all values of x. The area of the region between the graph of f and the x  axis is equal to 1.n1 2$$$$$$.$$ $$$8X 8 <A :??  8 :$D 0 8 6`X 3f>"`  g,$ 0 @Area = 1 0 2  8 c $A ;??0 8 8 ;$@  0H 8 0޽h ? 33G?___PPT10.=Q@+ײD' = @B Dv' = @BA?%,( < +O%,( < +D' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*8 %(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*8 D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*8 D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*8 n%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*8 nD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*8 nD' =%(Dc' =4@BB*BB%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =-g6B fade*<3<*8D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*8D' =+4 8?bCB#ppt_y+.1BCB#ppt_yB*Y3>B ppt_y<*8DV' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*8D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*8D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =-g6B fade*<3<*8+8+0+8C +   <I(  < < 0x  TProbability Density Function0 2( < 0||  u= is given by the area of the shaded region.>0 2>x < <A <??p <` < c $A =?? `   = < 0DO p0  ;b0 2 < 0, p  ;a0 2RB < s *D8cP ``RB  < s *D8c pB  < 0D8c0 ,$D  02  < 0>"` P,$D  0`  < c $A >?? >H < 0޽h ? 33___PPT10.Q@b+{D' = @B Dc' = @BA?%,( < +O%,( < +D' =%(%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* <%(D' =-s6Bwipe(left)*<3<* <D' =%(D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* <%(D' =-o6Bwipe(up)*<3<* <+ XP(    0 j FUniform Distribution 2(  0  :bA continuous rv X is said to have a uniform distribution on the interval [A, B] if the pdf of X isc 2$$$$$$$$$$$, H `  c $A ??0   H  0޽h ? ̙33 +(    0̣ P  sProbability for a Continuous rv 2 (  0T @ fIf X is a continuous rv, then for any number c, P(x = c) = 0. For any two numbers a and b with a < b,g 2$$)$$$$$$$$$$$$$$$$$P`  c $A ??   `  c $A ??@ `   `  c $A  ??P `   H  0޽h ? ̙33) @)(  @ @ 6( 8c"`0'  }94.2 Cumulative Distribution Functions and Expected Values(:0(206<H @ 0޽h ? 3380___PPT10. Pۘ tl(    0  P V$The Cumulative Distribution Function% 2%(m  0  aThe cumulative distribution function, F(x) for a continuous rv X is defined for every number x bynb 2&$$$$$$$$$<$`  c $A ??t  1  0x @ . GFor each x, F(x) is the area under the density curve to the left of x. nH 2 $$$$$$5$$$H  0޽h ? ̙33z *" (     0 P  #Using F(x) to Compute ProbabilitiesB$ 2(((((`   c $A ??0 "   0 P> HLLet X be a continuous rv with pdf f(x) and cdf F(x). 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