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प्रश्न
Solve the following problem :
Let X∼B(n,p) If E(X) = 5 and Var(X) = 2.5, find n and p.
उत्तर
Let X ~ B(n, p)
E(X) = 5 and Var (X) = 2.5 …[Given]
But E(X) = np = 5 and
Var (X) = npq = 2.5
∴ 5(q) = 2.5
∴ q = `(2.5)/(5) = (1)/(2)`
∴ p = 1 – q = `1 - (1)/(2) = (1)/(2)`
Now, np = 5
∴ `"n"(1/2)` = 5
∴ n = 10.
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