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Question
Let X be a discrete random variable whose probability distribution is defined as follows:
P(X = x) = `{{:("k"(x + 1), "for" x = 1"," 2"," 3"," 4),(2"k"x, "for" x = 5"," 6"," 7),(0, "Otherwise"):}`
where k is a constant. Calculate E(X)
Solution
Now the probability distribution is
| X | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| P(X) | `2/50` | `3/50` | `4/50` | `5/50` | `10/50` | `12/20` | `14/50` |
E(X) = `1 xx 2/50 + 2 xx 3/50 + 3 xx 4/50 + 4 xx 5/50 + 5 xx 10/50 + 6 xx 12/50 + 7 xx 14/50`
= `2/50 + 6/50 + 12/50 + 50/50 + 72/50 + 98/50`
= `260/50`
= `26/5`
= `5.2
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