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Question
Find the mean number of defective items in a sample of two items drawn one-by-one without replacement from an urn containing 6 items, which include 2 defective items. Assume that the items are identical in shape and size.
Solution
Let X denote the Random Variable defined by the number of defective items.
P(X = 0) = `4/6 xx 3/5 = 2/5`
P(X = 1) = `2 xx (2/6 xx 4/5) = 8/15`
P(X = 2) = `2/6 xx 1/5 = 1/15`
| xi | 0 | 1 | 2 |
| pi | `2/5` | `8/15` | `1/15` |
| pixi | 0 | `8/15` | `2/15` |
Mean = `sump_ix_i = 10/15 = 2/3`
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