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प्रश्न
The mean and standard deviation of a binomial variate X are respectively 6 and 2. Find P(X ≥ 2)
उत्तर
X ~ B(n, p)
Given, Mean = 6
Standard deviation = 2
np = 6, `sqrt("npq")` = 2
npq = 4
`"npq"/"np"= 4/6`
q = `2/3`
p = 1 – q = `1/3`
npq = 4
`n" xx 1/3 xx 2/3` = 4
n = 18
P(X ≥ 2) = 1 – P(X < 2)
= 1 – [P(X = 0) P(X = 1)]
= `1 - [""^18"C"_0 (1/3)^0 (2/3)^18 + ""^18"C"_1 (1/3)^1 (2/3)^17]`
= ` - (2/3)^17 xx 20/3`
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