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# If the range of X is the set {0,1,2,3,4,5,6,7,8} and P(X=x) as defined in the following table:

x | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|---|

P(X=x) | 0.06528 | 0.3870 | 0.03062 | 0.0968 | 0.06913 | 0.0968 | 0.04846 |
0.01252 |
0.1935 |

Determine the mean and variance.

**Solution:**

**Mean:**

E(x) = ∑ xᵢp(xᵢ)

∑ xᵢp(xᵢ) = 1(0.3870) + 2(0.038062) + 3(0.0968) + 4(0.06913) + 5(0.0968) + 6(0.04846) + 7(0.01252) + 8(0.1935)

∑ xᵢp(xᵢ) = 3.43672

Mean = 3.43672

**Variance:**

Variance = E(x²) - [E(x)]²

E(x²) = ∑ x²ᵢp(xᵢ)

∑ x²ᵢp(xᵢ) = 1²(0.3870) + 2²(0.038062) + 3²(0.0968) + 4²(0.06913) + 5²(0.0968) + 6²(0.04846) + 7²(0.01252) + 8²(0.1935)

∑ x²ᵢp(xᵢ) = 19.6488

∴ Variance = 19.6488 - (3.43672)² = 7.837755

## If the range of X is the set {0,1,2,3,4,5,6,7,8} and P(X=x) as defined in the following table:

x | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|---|

P(X=x) | 0.06528 | 0.3870 | 0.03062 | 0.0968 | 0.06913 | 0.0968 | 0.04846 |
0.01252 |
0.1935 |

Determine the mean and variance.

**Summary:**

Mean and Variance of the given table are 3.43672 and 7.837755 respectively.

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