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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) = {{:(1/10, x = 2"," 5),(1/5, x = 0"," 1"," 3"," 4):}`
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Solution
Probability mass function
| x | 0 | 1 | 2 | 3 | 4 | 5 |
| F(x) | `1/5` | `1/5` | `1/10` | `1/5` | `1/5` | `1/10 |
Mean: `mu = "E"("X")`
= `sum x f(x)`
= `0 xx 1/5 + 1 xx 1/5 + 2 xx 1/10 + 3 xx 1/5 + 4 xx 1/5 + 5 xx 1/10`
= `0 + 1/5 + 2/10 + 3/5 + 4/5 + 5/10`
= `23/10`
= 2.3
Variance: `"E"("X"^2)`
= `sum x^2 f(x)`
= `0^2 xx 1/5 + 1^2 xx 1/5 + 2^2 xx 1/10 + 3^2 xx 1/5 + 4^2 xx 1/5 + 5^2 xx 1/10`
= `0 + 1/5 + 4/10 + 9/5 + 16/5 + 25/10`
= `81/10`
= 8.1
Var(X)= E(X2) – [E(X)]2
= 8.1 – (2.3)2
= 8.1 – 5.29
= 2.81
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