Example 34 - Find mean of Binomial distribution B(4, 1/3) - Binomial Distribution

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  1. Chapter 13 Class 12 Probability
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Example 34 Find the mean of the Binomial distribution B(4, 1﷮3﷯) B(4, 1﷮3﷯) means Here, n = 4, p = 1﷮3﷯ So , q = 1 − 1﷮3﷯ = 2﷮3﷯ Hence, P (X = x) = 4Cx 𝟏﷮𝟑﷯﷯﷮𝒙﷯ 𝟐﷮𝟑﷯﷯﷮𝟒−𝒙﷯ Mean of distribution = P (X = x) = 4Cx 1﷮3﷯﷯﷮𝑥﷯ 2﷮3﷯﷯﷮4−𝑥﷯ Mean = = 0 + 1 × 4C1 1﷮3﷯﷯﷮1﷯ 2﷮3﷯﷯﷮3﷯+ 2 × 4C2 1﷮3﷯﷯﷮2﷯ 2﷮3﷯﷯﷮2﷯ + 3 × 4C3 1﷮3﷯﷯﷮3﷯ 2﷮3﷯﷯ + 4 × 4C4 1﷮3﷯﷯﷮4﷯ 2﷮3﷯﷯﷮0﷯ = 4 × 1﷮3﷯ × 8﷮27﷯ + 2 × 6 × 1﷮9﷯ × 4﷮9﷯ + 3 × 4 × 1﷮27﷯ × 2﷮3﷯ + 4 × 1﷮ 3﷮4﷯﷯ × 1 = 32﷮81﷯+ 48﷮81﷯+ 24﷮81﷯+ 4﷮81﷯ = 108﷮81﷯ = 𝟒﷮𝟑﷯

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