Three items are drawn in randomly from a population of 7 items. The item drawn may be defective or non-defective. A random variable is the occurrence of non-defective items. Total defective items in the population are two.
a.Make a frequency distribution table of the random variable.
Find the expected value of non-defective items in the random experiment.
Answers
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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