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Question
For the following probability distribution:
| X | 1 | 2 | 3 | 4 |
| P(X) | `1/10` | `3/10` | `3/10` | `2/5` |
E(X2) is equal to ______.
Options
3
5
7
10
Solution
For the following probability distribution:
| X | 1 | 2 | 3 | 4 |
| P(X) | `1/10` | `3/10` | `3/10` | `2/5` |
E(X2) is equal to 10.
Explanation:
We know that
E(X2) = `sum_("i" = 1)^"n" "P"_"i""X"_"i"^2`
= `1 xx 1/10 + 4 xx 1/5 + 9 xx 3/10 + 16 xx 2/5`
= `1/10 + 4/5 + 27/10 + 32/5`
= `28/10 + 36/5`
= `100/10`
= 10
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