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Question
The mean and variance of a random variable X having a binomial distribution are 6 and 3 respectively. The probability of variable X less than 2 is ______.
Options
`13/2048`
`13/4096`
`15/4096`
`25/2048`
MCQ
Fill in the Blanks
Solution
The mean and variance of a random variable X having a binomial distribution are 6 and 3 respectively. The probability of variable X less than 2 is `13/4096`.
Explanation:
np = 6, npq = 3
⇒ q = `1/2`, p = `1/2`, n = 12
∴ Required probability
= P(X < 2)
= `""^12"C"_0 (1/2)^0 (1/2)^12 + ""^12"C"_1 (1/2)^1 (1/2)^11`
= `13/2^12`
= `13/4096`
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Concept of Probability
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