Page 254 - Fundamentals of Probability and Statistics for Engineers
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Some Important Continuous Distributions                         237

                                                   1        2    ‡ k
                                                    1   k     1

                                                        2         ") 2
                      ‡ 1)                         2         ,"w
                      ‡                             1   k   1
                                                             1 ‡ k
                      ‡  ) 2 "                      v 2           1

                      "           2  6  2    2  6  2  1    ,  1   k    ")   1 ‡ k
                     ‡   ,      
         
                  ‡ "w
                                 u ‡   ,   u     ,                    2
                                                    v        "



                                                             0
                    0                               0        >
                     >           u         u        >  k     k
                    0,           0,        0,       0,       >",
                     >            >         >       >  v  0     ",w






                   ‡  ) x   1 "1   x)   1 ,  u)   1  <  y  <    exp [ "z   u)]g,        k    y  y  ,     exp  v    "   k 1      "  z   "   k    "     z  ,    "  w








                    "    " ) " )  1    expf  "y    exp [    "y   u)]g,  1    expf "z   u)  1  <  k    k‡1  v  y  v     z  k  ˆ w   "  w           exp
                    ˆ       x    ˆ         ˆ   z  <  ˆ
                    f X "x)     0  f Y "y)  f Z "z)   1  f Y "y)  f Z "z)




                            values:  max   min      max      min Type-III




                     Beta   Extreme  Type-I  (a)  Type-I  (b)  Type-II  (c)  (d)









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