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Question
For the random variable X with the given probability mass function as below, find the mean and variance.
`f(x) = {{:((4 - x)/6, x = 1"," 2"," 3),(0, "otherwise"):}`
Solution
Probability mass function
| x | 1 | 2 | 3 |
| F(x) | `1/2` | `1/3` | `1/6` |
Mean: `mu = "E"("X")`
= `sum x f(x)`
= `1 xx 1/2 + 2 xx 1/3 + 3 xx 1/6`
= `1/2 + 2/3 + 3/6`
= `10/6`
= 1.67
Variance: `"E"("X"^2)`
= `1^2 xx 1/2 + 2^2 xx 1/3 + 3^2 xx 1/6`
= `1/2 + 4/3 + 9/6`
= `20/6`
= 3.33
Var (X) = E(X2) – [E(X)]2
= 3.33 – (1.67)2
= 3.33 – 2.79
= 0.54
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