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

Sum

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

#### 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