# Let X ~ B(n, p) if E(X) = 5 and Var(X) = 2.5, find n and p. - Mathematics and Statistics

Sum

Let X ~ B(n, p) if E(X) = 5 and Var(X) = 2.5, find n and p.

#### Solution

X ~ B(n, p)

Given: E(X) = 5 and Var(X) = 2.5

np = 5  and npq = 2.5

∴ "npq"/"np" = 2.5/5

∴ q = 0.5 = 5/10 = 1/5

∴ p = 1 - p = 1 - 1/2 = 1/2

Substituting p = 1/2 in np = 5, we get

"n"(1/2) = 5

∴ n = 10

Hence, n = 10 and p = 1/2

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 2.2 | Page 253