Maharashtra State BoardHSC Arts 12th Board Exam
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Let X ~ B(n, p) if n = 10, E(X) = 5, find p and Var(X). - Mathematics and Statistics

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Sum

Let X ~ B(n, p) if n = 10, E(X) = 5, find p and Var(X).

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Solution

X ~ B(n, p)

Given: n = 10 and E(X) = 5

But E(X) = np      ∴ np = 5

∴ 10p = 5 

∴ p = `1/2`

∴ q = 1 - p = `1 - 1/2 = 1/2`

Var(X) = npq = `10(1/2)(1/2) = 2.5`

Hence, p = `1/2` and Var(X) = 2.5

Concept: Variance of Binomial Distribution (P.M.F.)
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APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 8 Binomial Distribution
Miscellaneous exercise 8 | Q 2.1 | Page 253
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