Math, asked by sarfarazsafdar678, 4 months ago


Q Three items are drawn in randomly from a population of 7 items. The item drawn may be defective or non-defective. Random variable is the occurrence of non-defective items.

Make a frequency distribution table of the random variable. [5]

Find the expected value of non-defective items in the random experiment. [5​

Answers

Answered by amitnrw
1

Given : Three items are drawn in randomly from a population of 7 items. The item drawn may be defective or non-defective. Random variable is the occurrence of non-defective items.  

To Find : Make a frequency distribution table of the random variable.  

Find the expected value of non-defective items in the random experiment.  

Solution:

The item drawn may be defective or non-defective

Each item drawn can be in 2 ways

defective  D   or non-defective  N

Total Ways     = 2 x 2  x 2  = 8

            1         2         3             Defectives    Non Defectives

           D         D         D                  3                     0

           D         D         N                  2                     1      

           D         N         D                  2                     1

           D         N         N                  1                      2      

           N         D         D                  2                     1

           N         D         N                  1                      2                  

           N         N         D                  1                      2

           N         N         N                  0                     3    

frequency distribution table of the Defective

       Defective                Frequency   Probability

              3                                 1                1/8  

              2                                 3               3/8

              1                                  3               3/8

              0                                 1                1/8

frequency distribution table of the random variable Non-Defective

      Non Defective                Frequency   Probability

              3                                 1               1/8

              2                                 3              3/8

              1                                  3              3/8

              0                                 1               1/8

expected value of non-defective items in the random experiment

= 3x 1/8  + 2 x 3/8  + 1 x3/8  + 0 x 1/8

= (3 + 6  + 3 + 0)/8

= 12/8

= 1.5

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