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Ex 13.5, 8 - Suppose X has binomial distribution B(6, 1/2) - Ex 13.5

Ex 13.5, 8 - Chapter 13 Class 12 Probability - Part 2


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Ex 13.5, 8 Suppose X has a binomial distribution B (6, 1﷮2﷯) . Show that X = 3 is the most likely outcome. (Hint : P(X = 3) is the maximum among all P(xi), xi = 0,1,2,3,4,5,6) B(6, 1﷮2﷯) means Here , n = 6, p = 𝟏﷮𝟐﷯ So , q = 1 − 1﷮2﷯ = 1﷮2﷯ Hence, P (X = x) = 6Cx 1﷮2﷯﷯﷮𝑥﷯ 1﷮2﷯﷯﷮6−𝑥﷯ P (X = x) = 6Cx 1﷮2﷯﷯﷮𝑥 + 6 − 𝑥﷯ P (X = x) = 6Cx 𝟏﷮𝟐﷯﷯﷮𝒙﷯ Hence, P (X = x) = 6Cx 1﷮2﷯﷯﷮𝑥﷯ We need to show that X = 3 is the most likely outcome. i.e. P(X = 3) is the maximum among P(X = 0) , P(X = 1), P(X = 2), P(X = 3), P(X = 4), P(X = 5), P(X = 6) Since P(X = 3) is maximum ∴ Most likely outcome is X = 3

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.