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Question
A discrete random variable X has the probability distribution given as below:
| X | 0.5 | 1 | 1.5 | 2 |
| P(X) | k | k2 | 2k2 | k |
Determine the mean of the distribution.
Solution
For a probability distribution, we know that if Pi ≥ 0
Mean of the distribution
E(X) = `sum_("i" = 1)^"n" "X"_"i""P"_"i"`
= 0.5k + 1.k2 + 1.5(2k2) + 2k
= `"k"/2 + "k"^2 + 3"k"^2 + 2"k"`
= `4"k"^2 + 5/2"k"`
= `4(1/3)^2 + 5/2(1/3)`
= `4/9 + 5/6`
= `23/18`
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